TSTP Solution File: NUM600+1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : NUM600+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 01:30:50 EDT 2024
% Result : Theorem 90.58s 36.86s
% Output : Refutation 91.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 145
% Syntax : Number of formulae : 980 ( 156 unt; 48 typ; 0 def)
% Number of atoms : 3203 (1104 equ; 0 cnn)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 8763 (1336 ~;1156 |; 350 &;5552 @)
% ( 22 <=>; 347 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 48 usr; 16 con; 0-3 aty)
% Number of variables : 829 ( 0 ^ 798 !; 31 ?; 829 :)
% Comments :
%------------------------------------------------------------------------------
thf(slcrc0_type,type,
slcrc0: $i ).
thf(aSet0_type,type,
aSet0: $i > $o ).
thf(aElementOf0_type,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_type,type,
aSubsetOf0: $i > $i > $o ).
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(sdtmndt0_type,type,
sdtmndt0: $i > $i > $i ).
thf(szNzAzT0_type,type,
szNzAzT0: $i ).
thf(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(isFinite0_type,type,
isFinite0: $i > $o ).
thf(szmzazxdt0_type,type,
szmzazxdt0: $i > $i ).
thf(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
thf(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
thf(slbdtsldtrb0_type,type,
slbdtsldtrb0: $i > $i > $i ).
thf(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
thf(aFunction0_type,type,
aFunction0: $i > $o ).
thf(sdtlbdtrb0_type,type,
sdtlbdtrb0: $i > $i > $i ).
thf(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
thf(sdtlpdtrp0_type,type,
sdtlpdtrp0: $i > $i > $i ).
thf(sdtlcdtrc0_type,type,
sdtlcdtrc0: $i > $i > $i ).
thf(sdtexdt0_type,type,
sdtexdt0: $i > $i > $i ).
thf(xO_type,type,
xO: $i ).
thf(xd_type,type,
xd: $i ).
thf(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
thf(xe_type,type,
xe: $i ).
thf(sz00_type,type,
sz00: $i ).
thf(xc_type,type,
xc: $i ).
thf(xS_type,type,
xS: $i ).
thf(xK_type,type,
xK: $i ).
thf(xT_type,type,
xT: $i ).
thf(isCountable0_type,type,
isCountable0: $i > $o ).
thf(xN_type,type,
xN: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(xk_type,type,
xk: $i ).
thf(xC_type,type,
xC: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i > $o ).
thf(sk3_type,type,
sk3: $i > $i > $i ).
thf(sk4_type,type,
sk4: $i > $i > $i ).
thf(sk5_type,type,
sk5: $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk8_type,type,
sk8: $i > $i > $i > $o ).
thf(sk9_type,type,
sk9: $i > $i > $i > $i ).
thf(sk10_type,type,
sk10: $i > $i > $i > $i ).
thf(sk11_type,type,
sk11: $i > $i > $i > $i ).
thf(sk31_type,type,
sk31: $i > $i ).
thf(1,conjecture,
! [A: $i] :
( ( aElementOf0 @ A @ xO )
=> ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( aElementOf0 @ A @ xO )
=> ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ B )
= A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(99,plain,
~ ! [A: $i] :
( ( aElementOf0 @ A @ xO )
=> ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(101,plain,
aElementOf0 @ sk1 @ xO,
inference(cnf,[status(esa)],[99]) ).
thf(38,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
thf(216,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(218,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) ),
inference(cnf,[status(esa)],[216]) ).
thf(20041,plain,
! [A: $i] :
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
| ( ( aElementOf0 @ sk1 @ xO )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[101,218]) ).
thf(20169,plain,
! [A: $i] :
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
| ( sk1 != A )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[20041]) ).
thf(20194,plain,
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ sk1 ) )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[20169]) ).
thf(81,axiom,
( ( aElementOf0 @ xk @ szNzAzT0 )
& ( ( szszuzczcdt0 @ xk )
= xK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
thf(506,plain,
( ( aElementOf0 @ xk @ szNzAzT0 )
& ( ( szszuzczcdt0 @ xk )
= xK ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(508,plain,
aElementOf0 @ xk @ szNzAzT0,
inference(cnf,[status(esa)],[506]) ).
thf(83,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( A = sz00 )
| ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
thf(513,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( A = sz00 )
| ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(515,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( A = sz00 )
| ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 ) ),
inference(cnf,[status(esa)],[513]) ).
thf(517,plain,
! [A: $i] :
( ( A = sz00 )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 ) ),
inference(lifteq,[status(thm)],[515]) ).
thf(872,plain,
! [A: $i] :
( ( A = sz00 )
| ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
| ( ( aElementOf0 @ xk @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[508,517]) ).
thf(873,plain,
( ( xk = sz00 )
| ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 ) ),
inference(pattern_uni,[status(thm)],[872:[bind(A,$thf( xk ))]]) ).
thf(30,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( B
= ( slbdtrb0 @ A ) )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
<=> ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).
thf(168,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( B
= ( slbdtrb0 @ A ) )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ B )
=> ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) )
& ( ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) )
=> ( aElementOf0 @ C @ B ) ) ) ) )
& ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ B )
=> ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) )
& ( ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) )
=> ( aElementOf0 @ C @ B ) ) ) )
=> ( B
= ( slbdtrb0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(169,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ! [B: $i] :
( ( B
= ( slbdtrb0 @ A ) )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) )
=> ( aElementOf0 @ C @ B ) ) ) )
& ! [B: $i] :
( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) )
=> ( aElementOf0 @ C @ B ) ) )
=> ( B
= ( slbdtrb0 @ A ) ) ) ) ),
inference(miniscope,[status(thm)],[168]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( B
!= ( slbdtrb0 @ A ) )
| ( aSet0 @ B ) ),
inference(cnf,[status(esa)],[169]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( B
!= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( aSet0 @ B ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(186,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( aSet0 @ ( slbdtrb0 @ A ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(7765,plain,
! [A: $i] :
( ( xk = sz00 )
| ( aSet0 @ ( slbdtrb0 @ A ) )
| ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[873,186]) ).
thf(7766,plain,
( ( xk = sz00 )
| ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) ) ),
inference(pattern_uni,[status(thm)],[7765:[bind(A,$thf( sk31 @ xk ))]]) ).
thf(76,axiom,
( ( aSubsetOf0 @ xS @ szNzAzT0 )
& ( isCountable0 @ xS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
thf(455,plain,
( ( aSubsetOf0 @ xS @ szNzAzT0 )
& ( isCountable0 @ xS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(457,plain,
aSubsetOf0 @ xS @ szNzAzT0,
inference(cnf,[status(esa)],[455]) ).
thf(48,axiom,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( A != slcrc0 ) )
=> ! [B: $i] :
( ( B
= ( szmzizndt0 @ A ) )
<=> ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMin) ).
thf(241,plain,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( A != slcrc0 ) )
=> ! [B: $i] :
( ( ( B
= ( szmzizndt0 @ A ) )
=> ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ B @ C ) ) ) )
& ( ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ B @ C ) ) )
=> ( B
= ( szmzizndt0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(242,plain,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( A != slcrc0 ) )
=> ( ! [B: $i] :
( ( B
= ( szmzizndt0 @ A ) )
=> ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ B @ C ) ) ) )
& ! [B: $i] :
( ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ B @ C ) ) )
=> ( B
= ( szmzizndt0 @ A ) ) ) ) ),
inference(miniscope,[status(thm)],[241]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ( A = slcrc0 )
| ( B
!= ( szmzizndt0 @ A ) )
| ( aElementOf0 @ B @ A ) ),
inference(cnf,[status(esa)],[242]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( A = slcrc0 )
| ( B
!= ( szmzizndt0 @ A ) )
| ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ( aElementOf0 @ B @ A ) ),
inference(lifteq,[status(thm)],[244]) ).
thf(250,plain,
! [A: $i] :
( ( A = slcrc0 )
| ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ( aElementOf0 @ ( szmzizndt0 @ A ) @ A ) ),
inference(simp,[status(thm)],[249]) ).
thf(30071,plain,
! [A: $i] :
( ( A = slcrc0 )
| ( aElementOf0 @ ( szmzizndt0 @ A ) @ A )
| ( ( aSubsetOf0 @ xS @ szNzAzT0 )
!= ( aSubsetOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,250]) ).
thf(30072,plain,
( ( xS = slcrc0 )
| ( aElementOf0 @ ( szmzizndt0 @ xS ) @ xS ) ),
inference(pattern_uni,[status(thm)],[30071:[bind(A,$thf( xS ))]]) ).
thf(456,plain,
isCountable0 @ xS,
inference(cnf,[status(esa)],[455]) ).
thf(11,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
thf(123,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(124,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isCountable0 @ A )
| ( A != slcrc0 ) ),
inference(cnf,[status(esa)],[123]) ).
thf(125,plain,
! [A: $i] :
( ( A != slcrc0 )
| ~ ( aSet0 @ A )
| ~ ( isCountable0 @ A ) ),
inference(lifteq,[status(thm)],[124]) ).
thf(126,plain,
( ~ ( aSet0 @ slcrc0 )
| ~ ( isCountable0 @ slcrc0 ) ),
inference(simp,[status(thm)],[125]) ).
thf(61,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
thf(364,plain,
! [A: $i] :
( ( ( A = slcrc0 )
=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) )
& ( ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) )
=> ( A = slcrc0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(365,plain,
( ! [A: $i] :
( ( A = slcrc0 )
=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) )
& ! [A: $i] :
( ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) )
=> ( A = slcrc0 ) ) ),
inference(miniscope,[status(thm)],[364]) ).
thf(367,plain,
! [A: $i] :
( ( A != slcrc0 )
| ( aSet0 @ A ) ),
inference(cnf,[status(esa)],[365]) ).
thf(371,plain,
! [A: $i] :
( ( A != slcrc0 )
| ( aSet0 @ A ) ),
inference(lifteq,[status(thm)],[367]) ).
thf(372,plain,
aSet0 @ slcrc0,
inference(simp,[status(thm)],[371]) ).
thf(646,plain,
( ~ $true
| ~ ( isCountable0 @ slcrc0 ) ),
inference(rewrite,[status(thm)],[126,372]) ).
thf(647,plain,
~ ( isCountable0 @ slcrc0 ),
inference(simp,[status(thm)],[646]) ).
thf(659,plain,
( ( isCountable0 @ xS )
!= ( isCountable0 @ slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[456,647]) ).
thf(660,plain,
xS != slcrc0,
inference(simp,[status(thm)],[659]) ).
thf(34726,plain,
aElementOf0 @ ( szmzizndt0 @ xS ) @ xS,
inference(simplifyReflect,[status(thm)],[30072,660]) ).
thf(16,axiom,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
thf(136,plain,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(137,plain,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
inference(lifteq,[status(thm)],[136]) ).
thf(7762,plain,
! [A: $i] :
( ( aSet0 @ ( slbdtrb0 @ A ) )
| ( ( aElementOf0 @ sk1 @ xO )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[101,186]) ).
thf(7807,plain,
! [A: $i] :
( ( aSet0 @ ( slbdtrb0 @ A ) )
| ( sk1 != A )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[7762]) ).
thf(7814,plain,
( ( aSet0 @ ( slbdtrb0 @ sk1 ) )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[7807]) ).
thf(15,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
thf(134,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(135,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ( aSubsetOf0 @ A @ A ) ),
inference(cnf,[status(esa)],[134]) ).
thf(8218,plain,
! [A: $i] :
( ( xO != szNzAzT0 )
| ( aSubsetOf0 @ A @ A )
| ( ( aSet0 @ ( slbdtrb0 @ sk1 ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7814,135]) ).
thf(8219,plain,
( ( xO != szNzAzT0 )
| ( aSubsetOf0 @ ( slbdtrb0 @ sk1 ) @ ( slbdtrb0 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[8218:[bind(A,$thf( slbdtrb0 @ sk1 ))]]) ).
thf(14127,plain,
( ( xO != szNzAzT0 )
| ( aSubsetOf0 @ ( slbdtrb0 @ sk1 ) @ slcrc0 )
| ( ( slbdtrb0 @ sk1 )
!= ( slbdtrb0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[137,8219]) ).
thf(14220,plain,
( ( aSubsetOf0 @ ( slbdtrb0 @ sk1 ) @ slcrc0 )
| ( xO != szNzAzT0 )
| ( sk1 != sz00 ) ),
inference(simp,[status(thm)],[14127]) ).
thf(60,axiom,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
thf(361,plain,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(363,plain,
aSet0 @ szNzAzT0,
inference(cnf,[status(esa)],[361]) ).
thf(13,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardS) ).
thf(130,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(131,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
inference(cnf,[status(esa)],[130]) ).
thf(1368,plain,
! [A: $i] :
( ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ szNzAzT0 )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[363,131]) ).
thf(1369,plain,
aElement0 @ ( sbrdtbr0 @ szNzAzT0 ),
inference(pattern_uni,[status(thm)],[1368:[bind(A,$thf( szNzAzT0 ))]]) ).
thf(17,axiom,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3520) ).
thf(138,plain,
xK != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtpldt0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
thf(518,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtpldt0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) ) )
& ( ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) ) )
& ( ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtpldt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(57,axiom,
aElementOf0 @ xK @ szNzAzT0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
thf(325,plain,
aElementOf0 @ xK @ szNzAzT0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(861,plain,
! [A: $i] :
( ( A = sz00 )
| ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
| ( ( aElementOf0 @ xK @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[325,517]) ).
thf(862,plain,
( ( xK = sz00 )
| ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 ) ),
inference(pattern_uni,[status(thm)],[861:[bind(A,$thf( xK ))]]) ).
thf(12,axiom,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
thf(127,plain,
xK != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(128,plain,
xK != sz00,
inference(polarity_switch,[status(thm)],[127]) ).
thf(129,plain,
xK != sz00,
inference(lifteq,[status(thm)],[128]) ).
thf(1560,plain,
aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0,
inference(simplifyReflect,[status(thm)],[862,129]) ).
thf(7772,plain,
! [A: $i] :
( ( aSet0 @ ( slbdtrb0 @ A ) )
| ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[1560,186]) ).
thf(7773,plain,
aSet0 @ ( slbdtrb0 @ ( sk31 @ xK ) ),
inference(pattern_uni,[status(thm)],[7772:[bind(A,$thf( sk31 @ xK ))]]) ).
thf(7989,plain,
! [A: $i] :
( ( aSubsetOf0 @ A @ A )
| ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xK ) ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7773,135]) ).
thf(7990,plain,
aSubsetOf0 @ ( slbdtrb0 @ ( sk31 @ xK ) ) @ ( slbdtrb0 @ ( sk31 @ xK ) ),
inference(pattern_uni,[status(thm)],[7989:[bind(A,$thf( slbdtrb0 @ ( sk31 @ xK ) ))]]) ).
thf(362,plain,
isCountable0 @ szNzAzT0,
inference(cnf,[status(esa)],[361]) ).
thf(8,axiom,
isFinite0 @ slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
thf(115,plain,
isFinite0 @ slcrc0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7769,plain,
! [A: $i] :
( ( aSet0 @ ( slbdtrb0 @ A ) )
| ( ( aElementOf0 @ xK @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[325,186]) ).
thf(7770,plain,
aSet0 @ ( slbdtrb0 @ xK ),
inference(pattern_uni,[status(thm)],[7769:[bind(A,$thf( xK ))]]) ).
thf(27,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
thf(158,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(159,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isCountable0 @ A )
| ~ ( isFinite0 @ A ) ),
inference(cnf,[status(esa)],[158]) ).
thf(7839,plain,
! [A: $i] :
( ~ ( isCountable0 @ A )
| ~ ( isFinite0 @ A )
| ( ( aSet0 @ ( slbdtrb0 @ xK ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7770,159]) ).
thf(7840,plain,
( ~ ( isCountable0 @ ( slbdtrb0 @ xK ) )
| ~ ( isFinite0 @ ( slbdtrb0 @ xK ) ) ),
inference(pattern_uni,[status(thm)],[7839:[bind(A,$thf( slbdtrb0 @ xK ))]]) ).
thf(19626,plain,
( ~ ( isCountable0 @ ( slbdtrb0 @ xK ) )
| ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,7840]) ).
thf(19734,plain,
( ~ ( isCountable0 @ ( slbdtrb0 @ xK ) )
| ( ( slbdtrb0 @ xK )
!= slcrc0 ) ),
inference(simp,[status(thm)],[19626]) ).
thf(29209,plain,
( ( ( slbdtrb0 @ xK )
!= slcrc0 )
| ( ( isCountable0 @ ( slbdtrb0 @ xK ) )
!= ( isCountable0 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[362,19734]) ).
thf(29267,plain,
( ( ( slbdtrb0 @ xK )
!= slcrc0 )
| ( ( slbdtrb0 @ xK )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[29209]) ).
thf(4285,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isFinite0 @ A )
| ( ( isCountable0 @ xS )
!= ( isCountable0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[456,159]) ).
thf(4286,plain,
( ~ ( aSet0 @ xS )
| ~ ( isFinite0 @ xS ) ),
inference(pattern_uni,[status(thm)],[4285:[bind(A,$thf( xS ))]]) ).
thf(8023,plain,
( ~ ( isFinite0 @ xS )
| ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xK ) ) )
!= ( aSet0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[7773,4286]) ).
thf(8030,plain,
( ~ ( isFinite0 @ xS )
| ( ( slbdtrb0 @ ( sk31 @ xK ) )
!= xS ) ),
inference(simp,[status(thm)],[8023]) ).
thf(1671,plain,
! [A: $i] :
( ( aSubsetOf0 @ A @ A )
| ( ( aSet0 @ szNzAzT0 )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[363,135]) ).
thf(1672,plain,
aSubsetOf0 @ szNzAzT0 @ szNzAzT0,
inference(pattern_uni,[status(thm)],[1671:[bind(A,$thf( szNzAzT0 ))]]) ).
thf(29942,plain,
! [A: $i] :
( ( A = slcrc0 )
| ( aElementOf0 @ ( szmzizndt0 @ A ) @ A )
| ( ( aSubsetOf0 @ szNzAzT0 @ szNzAzT0 )
!= ( aSubsetOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[1672,250]) ).
thf(29943,plain,
( ( szNzAzT0 = slcrc0 )
| ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 ) ),
inference(pattern_uni,[status(thm)],[29942:[bind(A,$thf( szNzAzT0 ))]]) ).
thf(652,plain,
( ( isCountable0 @ szNzAzT0 )
!= ( isCountable0 @ slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[362,647]) ).
thf(654,plain,
szNzAzT0 != slcrc0,
inference(simp,[status(thm)],[652]) ).
thf(31786,plain,
aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0,
inference(simplifyReflect,[status(thm)],[29943,654]) ).
thf(31911,plain,
! [A: $i] :
( ( aSet0 @ ( slbdtrb0 @ A ) )
| ( ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[31786,186]) ).
thf(31912,plain,
aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ),
inference(pattern_uni,[status(thm)],[31911:[bind(A,$thf( szmzizndt0 @ szNzAzT0 ))]]) ).
thf(34099,plain,
( ~ ( isFinite0 @ xS )
| ( ( aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ) )
!= ( aSet0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[31912,4286]) ).
thf(34103,plain,
( ~ ( isFinite0 @ xS )
| ( ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) )
!= xS ) ),
inference(simp,[status(thm)],[34099]) ).
thf(44,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( isFinite0 @ A )
& ( aElementOf0 @ B @ A ) )
=> ( ( szszuzczcdt0 @ ( sbrdtbr0 @ ( sdtmndt0 @ A @ B ) ) )
= ( sbrdtbr0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
thf(232,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( isFinite0 @ A )
& ( aElementOf0 @ B @ A ) )
=> ( ( szszuzczcdt0 @ ( sbrdtbr0 @ ( sdtmndt0 @ A @ B ) ) )
= ( sbrdtbr0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isFinite0 @ A )
| ~ ( aElementOf0 @ B @ A )
| ( ( szszuzczcdt0 @ ( sbrdtbr0 @ ( sdtmndt0 @ A @ B ) ) )
= ( sbrdtbr0 @ A ) ) ),
inference(cnf,[status(esa)],[232]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( ( szszuzczcdt0 @ ( sbrdtbr0 @ ( sdtmndt0 @ A @ B ) ) )
= ( sbrdtbr0 @ A ) )
| ~ ( aSet0 @ A )
| ~ ( isFinite0 @ A )
| ~ ( aElementOf0 @ B @ A ) ),
inference(lifteq,[status(thm)],[233]) ).
thf(9572,plain,
! [A: $i] :
( ( xk = sz00 )
| ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7766,131]) ).
thf(9573,plain,
( ( xk = sz00 )
| ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) ) ) ),
inference(pattern_uni,[status(thm)],[9572:[bind(A,$thf( slbdtrb0 @ ( sk31 @ xk ) ))]]) ).
thf(20055,plain,
! [A: $i] :
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
| ( ( aElementOf0 @ xK @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[325,218]) ).
thf(20056,plain,
isCountable0 @ ( sdtlpdtrp0 @ xN @ xK ),
inference(pattern_uni,[status(thm)],[20055:[bind(A,$thf( xK ))]]) ).
thf(7778,plain,
! [A: $i] :
( ( aSet0 @ ( slbdtrb0 @ A ) )
| ( ( aElementOf0 @ xk @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[508,186]) ).
thf(7779,plain,
aSet0 @ ( slbdtrb0 @ xk ),
inference(pattern_uni,[status(thm)],[7778:[bind(A,$thf( xk ))]]) ).
thf(7913,plain,
! [A: $i] :
( ( aSubsetOf0 @ A @ A )
| ( ( aSet0 @ ( slbdtrb0 @ xk ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7779,135]) ).
thf(7914,plain,
aSubsetOf0 @ ( slbdtrb0 @ xk ) @ ( slbdtrb0 @ xk ),
inference(pattern_uni,[status(thm)],[7913:[bind(A,$thf( slbdtrb0 @ xk ))]]) ).
thf(9286,plain,
( ( aSubsetOf0 @ slcrc0 @ ( slbdtrb0 @ xk ) )
| ( ( slbdtrb0 @ xk )
!= ( slbdtrb0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[137,7914]) ).
thf(9351,plain,
( ( aSubsetOf0 @ slcrc0 @ ( slbdtrb0 @ xk ) )
| ( xk != sz00 ) ),
inference(simp,[status(thm)],[9286]) ).
thf(29,axiom,
( ( aFunction0 @ xe )
& ( ( szDzozmdt0 @ xe )
= szNzAzT0 )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( sdtlpdtrp0 @ xe @ A )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
thf(162,plain,
( ( aFunction0 @ xe )
& ( ( szDzozmdt0 @ xe )
= szNzAzT0 )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( sdtlpdtrp0 @ xe @ A )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(163,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( ( sdtlpdtrp0 @ xe @ A )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ),
inference(cnf,[status(esa)],[162]) ).
thf(166,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 ) ),
inference(lifteq,[status(thm)],[163]) ).
thf(4720,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
| ( ( aElementOf0 @ xK @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[325,166]) ).
thf(4721,plain,
( ( sdtlpdtrp0 @ xe @ xK )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xK ) ) ),
inference(pattern_uni,[status(thm)],[4720:[bind(A,$thf( xK ))]]) ).
thf(20223,plain,
( ( isCountable0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xK ) ) )
| ( ( sdtlpdtrp0 @ xN @ xK )
!= ( sdtlpdtrp0 @ xe @ xK ) ) ),
inference(paramod_ordered,[status(thm)],[4721,20056]) ).
thf(20285,plain,
( ( isCountable0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xK ) ) )
| ( xN != xe )
| ( xK != xK ) ),
inference(simp,[status(thm)],[20223]) ).
thf(20310,plain,
( ( isCountable0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xK ) ) )
| ( xN != xe ) ),
inference(simp,[status(thm)],[20285]) ).
thf(69577,plain,
( ( isCountable0 @ ( sdtlpdtrp0 @ xe @ xK ) )
| ( xN != xe )
| ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xK ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xK ) ) ) ),
inference(paramod_ordered,[status(thm)],[4721,20310]) ).
thf(69578,plain,
( ( isCountable0 @ ( sdtlpdtrp0 @ xe @ xK ) )
| ( xN != xe ) ),
inference(pattern_uni,[status(thm)],[69577:[]]) ).
thf(69861,plain,
( ( xN != xe )
| ( ( isCountable0 @ ( sdtlpdtrp0 @ xe @ xK ) )
!= ( isCountable0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[69578,647]) ).
thf(69974,plain,
( ( xN != xe )
| ( ( sdtlpdtrp0 @ xe @ xK )
!= slcrc0 ) ),
inference(simp,[status(thm)],[69861]) ).
thf(9,axiom,
( ( aFunction0 @ xc )
& ( ( szDzozmdt0 @ xc )
= ( slbdtsldtrb0 @ xS @ xK ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) @ xT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
thf(116,plain,
( ( aFunction0 @ xc )
& ( ( szDzozmdt0 @ xc )
= ( slbdtsldtrb0 @ xS @ xK ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) @ xT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(119,plain,
aFunction0 @ xc,
inference(cnf,[status(esa)],[116]) ).
thf(10,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
thf(121,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(122,plain,
! [A: $i] :
( ~ ( aFunction0 @ A )
| ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
inference(cnf,[status(esa)],[121]) ).
thf(1250,plain,
! [A: $i] :
( ( aSet0 @ ( szDzozmdt0 @ A ) )
| ( ( aFunction0 @ xc )
!= ( aFunction0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[119,122]) ).
thf(1251,plain,
aSet0 @ ( szDzozmdt0 @ xc ),
inference(pattern_uni,[status(thm)],[1250:[bind(A,$thf( xc ))]]) ).
thf(4297,plain,
! [A: $i] :
( ~ ( isCountable0 @ A )
| ~ ( isFinite0 @ A )
| ( ( aSet0 @ ( szDzozmdt0 @ xc ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1251,159]) ).
thf(4298,plain,
( ~ ( isCountable0 @ ( szDzozmdt0 @ xc ) )
| ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) ) ),
inference(pattern_uni,[status(thm)],[4297:[bind(A,$thf( szDzozmdt0 @ xc ))]]) ).
thf(7325,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( ( isCountable0 @ ( szDzozmdt0 @ xc ) )
!= ( isCountable0 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[362,4298]) ).
thf(7368,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xc )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[7325]) ).
thf(118,plain,
( ( szDzozmdt0 @ xc )
= ( slbdtsldtrb0 @ xS @ xK ) ),
inference(cnf,[status(esa)],[116]) ).
thf(120,plain,
( ( slbdtsldtrb0 @ xS @ xK )
= ( szDzozmdt0 @ xc ) ),
inference(lifteq,[status(thm)],[118]) ).
thf(507,plain,
( ( szszuzczcdt0 @ xk )
= xK ),
inference(cnf,[status(esa)],[506]) ).
thf(509,plain,
( ( szszuzczcdt0 @ xk )
= xK ),
inference(lifteq,[status(thm)],[507]) ).
thf(3357,plain,
( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
| ( ( szszuzczcdt0 @ sz00 )
= xK )
| ( xk != xk ) ),
inference(paramod_ordered,[status(thm)],[873,509]) ).
thf(3358,plain,
( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
| ( ( szszuzczcdt0 @ sz00 )
= xK ) ),
inference(pattern_uni,[status(thm)],[3357:[]]) ).
thf(7780,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ sz00 )
= xK )
| ( aSet0 @ ( slbdtrb0 @ A ) )
| ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[3358,186]) ).
thf(7781,plain,
( ( ( szszuzczcdt0 @ sz00 )
= xK )
| ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) ) ),
inference(pattern_uni,[status(thm)],[7780:[bind(A,$thf( sk31 @ xk ))]]) ).
thf(33,axiom,
aSubsetOf0 @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) @ xT,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4758) ).
thf(202,plain,
aSubsetOf0 @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) @ xT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(3381,plain,
! [A: $i] :
( ( xk = sz00 )
| ( A = sz00 )
| ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
| ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[873,517]) ).
thf(3382,plain,
( ( xk = sz00 )
| ( ( sk31 @ xk )
= sz00 )
| ( aElementOf0 @ ( sk31 @ ( sk31 @ xk ) ) @ szNzAzT0 ) ),
inference(pattern_uni,[status(thm)],[3381:[bind(A,$thf( sk31 @ xk ))]]) ).
thf(4713,plain,
! [A: $i] :
( ( xk = sz00 )
| ( ( sdtlpdtrp0 @ xe @ A )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
| ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[873,166]) ).
thf(4714,plain,
( ( xk = sz00 )
| ( ( sdtlpdtrp0 @ xe @ ( sk31 @ xk ) )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xk ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4713:[bind(A,$thf( sk31 @ xk ))]]) ).
thf(8212,plain,
! [A: $i] :
( ( xO != szNzAzT0 )
| ~ ( isCountable0 @ A )
| ~ ( isFinite0 @ A )
| ( ( aSet0 @ ( slbdtrb0 @ sk1 ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7814,159]) ).
thf(8213,plain,
( ( xO != szNzAzT0 )
| ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
| ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[8212:[bind(A,$thf( slbdtrb0 @ sk1 ))]]) ).
thf(24422,plain,
( ( xO != szNzAzT0 )
| ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
| ( ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,8213]) ).
thf(24557,plain,
( ( xO != szNzAzT0 )
| ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
| ( ( slbdtrb0 @ sk1 )
!= slcrc0 ) ),
inference(simp,[status(thm)],[24422]) ).
thf(59063,plain,
( ( xO != szNzAzT0 )
| ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
| ( ( slbdtrb0 @ sk1 )
!= ( slbdtrb0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[137,24557]) ).
thf(59208,plain,
( ( xO != szNzAzT0 )
| ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
| ( sk1 != sz00 ) ),
inference(simp,[status(thm)],[59063]) ).
thf(59348,plain,
( ( xO != szNzAzT0 )
| ( sk1 != sz00 )
| ( ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
!= ( isCountable0 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[362,59208]) ).
thf(59412,plain,
( ( xO != szNzAzT0 )
| ( sk1 != sz00 )
| ( ( slbdtrb0 @ sk1 )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[59348]) ).
thf(20,axiom,
( ( aSet0 @ xT )
& ( isFinite0 @ xT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
thf(145,plain,
( ( aSet0 @ xT )
& ( isFinite0 @ xT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(147,plain,
aSet0 @ xT,
inference(cnf,[status(esa)],[145]) ).
thf(4295,plain,
! [A: $i] :
( ~ ( isCountable0 @ A )
| ~ ( isFinite0 @ A )
| ( ( aSet0 @ xT )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,159]) ).
thf(4296,plain,
( ~ ( isCountable0 @ xT )
| ~ ( isFinite0 @ xT ) ),
inference(pattern_uni,[status(thm)],[4295:[bind(A,$thf( xT ))]]) ).
thf(146,plain,
isFinite0 @ xT,
inference(cnf,[status(esa)],[145]) ).
thf(4359,plain,
( ~ ( isCountable0 @ xT )
| ~ $true ),
inference(rewrite,[status(thm)],[4296,146]) ).
thf(4360,plain,
~ ( isCountable0 @ xT ),
inference(simp,[status(thm)],[4359]) ).
thf(4362,plain,
( ( isCountable0 @ xT )
!= ( isCountable0 @ xS ) ),
inference(paramod_ordered,[status(thm)],[456,4360]) ).
thf(4376,plain,
xT != xS,
inference(simp,[status(thm)],[4362]) ).
thf(217,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 ) ),
inference(cnf,[status(esa)],[216]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtmndt0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
thf(262,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtmndt0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) ) )
& ( ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) ) )
& ( ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtmndt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(263,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ( ! [C: $i] :
( ( C
= ( sdtmndt0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) ) )
& ! [D: $i] :
( ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
& ! [C: $i] :
( ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) ) )
& ! [D: $i] :
( ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) )
=> ( aElementOf0 @ D @ C ) ) )
=> ( C
= ( sdtmndt0 @ A @ B ) ) ) ) ),
inference(miniscope,[status(thm)],[262]) ).
thf(269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ( C
!= ( sdtmndt0 @ A @ B ) )
| ~ ( aElement0 @ D )
| ~ ( aElementOf0 @ D @ A )
| ( D = B )
| ( aElementOf0 @ D @ C ) ),
inference(cnf,[status(esa)],[263]) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( sdtmndt0 @ A @ B ) )
| ( D = B )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElement0 @ D )
| ~ ( aElementOf0 @ D @ A )
| ( aElementOf0 @ D @ C ) ),
inference(lifteq,[status(thm)],[269]) ).
thf(276,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElement0 @ C )
| ~ ( aElementOf0 @ C @ A )
| ( aElementOf0 @ C @ ( sdtmndt0 @ A @ B ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(4710,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
| ( ( aElementOf0 @ xk @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[508,166]) ).
thf(4711,plain,
( ( sdtlpdtrp0 @ xe @ xk )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xk ) ) ),
inference(pattern_uni,[status(thm)],[4710:[bind(A,$thf( xk ))]]) ).
thf(4,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( sbrdtbr0 @ A )
= sz00 )
<=> ( A = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
thf(105,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( ( sbrdtbr0 @ A )
= sz00 )
=> ( A = slcrc0 ) )
& ( ( A = slcrc0 )
=> ( ( sbrdtbr0 @ A )
= sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(106,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ( ( sbrdtbr0 @ A )
!= sz00 )
| ( A = slcrc0 ) ),
inference(cnf,[status(esa)],[105]) ).
thf(108,plain,
! [A: $i] :
( ( ( sbrdtbr0 @ A )
!= sz00 )
| ( A = slcrc0 )
| ~ ( aSet0 @ A ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(667,plain,
! [A: $i] :
( ( ( sbrdtbr0 @ A )
!= sz00 )
| ( A = slcrc0 )
| ( ( aSet0 @ szNzAzT0 )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[363,108]) ).
thf(668,plain,
( ( ( sbrdtbr0 @ szNzAzT0 )
!= sz00 )
| ( szNzAzT0 = slcrc0 ) ),
inference(pattern_uni,[status(thm)],[667:[bind(A,$thf( szNzAzT0 ))]]) ).
thf(3745,plain,
( ( sbrdtbr0 @ szNzAzT0 )
!= sz00 ),
inference(simplifyReflect,[status(thm)],[668,654]) ).
thf(41,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRefl) ).
thf(225,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(226,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( sdtlseqdt0 @ A @ A ) ),
inference(cnf,[status(esa)],[225]) ).
thf(22969,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aElementOf0 @ xk @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[508,226]) ).
thf(22970,plain,
sdtlseqdt0 @ xk @ xk,
inference(pattern_uni,[status(thm)],[22969:[bind(A,$thf( xk ))]]) ).
thf(31,axiom,
( ( aSet0 @ xO )
& ( isCountable0 @ xO ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).
thf(197,plain,
( ( aSet0 @ xO )
& ( isCountable0 @ xO ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(199,plain,
aSet0 @ xO,
inference(cnf,[status(esa)],[197]) ).
thf(1669,plain,
! [A: $i] :
( ( aSubsetOf0 @ A @ A )
| ( ( aSet0 @ xO )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[199,135]) ).
thf(1670,plain,
aSubsetOf0 @ xO @ xO,
inference(pattern_uni,[status(thm)],[1669:[bind(A,$thf( xO ))]]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( A != slcrc0 )
| ~ ( aElementOf0 @ B @ A ) ),
inference(cnf,[status(esa)],[365]) ).
thf(373,plain,
! [B: $i,A: $i] :
( ( A != slcrc0 )
| ~ ( aElementOf0 @ B @ A ) ),
inference(lifteq,[status(thm)],[368]) ).
thf(374,plain,
! [A: $i] :
~ ( aElementOf0 @ A @ slcrc0 ),
inference(simp,[status(thm)],[373]) ).
thf(605,plain,
! [A: $i] :
( ( aElementOf0 @ sk1 @ xO )
!= ( aElementOf0 @ A @ slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[101,374]) ).
thf(606,plain,
! [A: $i] :
( ( sk1 != A )
| ( xO != slcrc0 ) ),
inference(simp,[status(thm)],[605]) ).
thf(607,plain,
xO != slcrc0,
inference(simp,[status(thm)],[606]) ).
thf(30910,plain,
! [A: $i] :
( ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ( aElementOf0 @ ( szmzizndt0 @ A ) @ A )
| ( A != xO ) ),
inference(paramod_ordered,[status(thm)],[250,607]) ).
thf(30911,plain,
( ~ ( aSubsetOf0 @ xO @ szNzAzT0 )
| ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO ) ),
inference(pattern_uni,[status(thm)],[30910:[bind(A,$thf( xO ))]]) ).
thf(32016,plain,
( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
| ( ( aSubsetOf0 @ xO @ xO )
!= ( aSubsetOf0 @ xO @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[1670,30911]) ).
thf(32050,plain,
( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
| ( xO != xO )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[32016]) ).
thf(32083,plain,
( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[32050]) ).
thf(94,axiom,
( ( aFunction0 @ xN )
& ( ( szDzozmdt0 @ xN )
= szNzAzT0 )
& ( ( sdtlpdtrp0 @ xN @ sz00 )
= xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
=> ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
thf(587,plain,
( ( aFunction0 @ xN )
& ( ( szDzozmdt0 @ xN )
= szNzAzT0 )
& ( ( sdtlpdtrp0 @ xN @ sz00 )
= xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
=> ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(588,plain,
( ( sdtlpdtrp0 @ xN @ sz00 )
= xS ),
inference(cnf,[status(esa)],[587]) ).
thf(594,plain,
( ( sdtlpdtrp0 @ xN @ sz00 )
= xS ),
inference(lifteq,[status(thm)],[588]) ).
thf(47,axiom,
aElementOf0 @ sz00 @ szNzAzT0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
thf(240,plain,
aElementOf0 @ sz00 @ szNzAzT0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(100,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xe @ A )
!= sk1 ) ),
inference(cnf,[status(esa)],[99]) ).
thf(102,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
!= sk1 )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(672,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
!= sk1 )
| ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( aElementOf0 @ sz00 @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[240,102]) ).
thf(673,plain,
( ( ( sdtlpdtrp0 @ xe @ sz00 )
!= sk1 )
| ~ ( aElementOf0 @ sz00 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
inference(pattern_uni,[status(thm)],[672:[bind(A,$thf( sz00 ))]]) ).
thf(785,plain,
( ( sk1 != xS )
| ~ ( aElementOf0 @ sz00 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xN @ sz00 )
!= ( sdtlpdtrp0 @ xe @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[594,673]) ).
thf(790,plain,
( ( sk1 != xS )
| ~ ( aElementOf0 @ sz00 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( xN != xe )
| ( sz00 != sz00 ) ),
inference(simp,[status(thm)],[785]) ).
thf(797,plain,
( ( sk1 != xS )
| ~ ( aElementOf0 @ sz00 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( xN != xe ) ),
inference(simp,[status(thm)],[790]) ).
thf(715,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
!= sk1 )
| ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( aElementOf0 @ xk @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[508,102]) ).
thf(716,plain,
( ( ( sdtlpdtrp0 @ xe @ xk )
!= sk1 )
| ~ ( aElementOf0 @ xk @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
inference(pattern_uni,[status(thm)],[715:[bind(A,$thf( xk ))]]) ).
thf(804,plain,
( ( ( sdtlpdtrp0 @ xe @ xk )
!= sk1 )
| ( ( aElementOf0 @ xk @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
!= ( aElementOf0 @ xk @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[508,716]) ).
thf(811,plain,
( ( ( sdtlpdtrp0 @ xe @ xk )
!= sk1 )
| ( xk != xk )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[804]) ).
thf(814,plain,
( ( ( sdtlpdtrp0 @ xe @ xk )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[811]) ).
thf(24448,plain,
( ( xO != szNzAzT0 )
| ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
| ( ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
!= ( isCountable0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[456,8213]) ).
thf(24560,plain,
( ( xO != szNzAzT0 )
| ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
| ( ( slbdtrb0 @ sk1 )
!= xS ) ),
inference(simp,[status(thm)],[24448]) ).
thf(4754,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
| ( ( aElementOf0 @ sz00 @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[240,166]) ).
thf(4755,plain,
( ( sdtlpdtrp0 @ xe @ sz00 )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[4754:[bind(A,$thf( sz00 ))]]) ).
thf(5090,plain,
( ( sdtlpdtrp0 @ xe @ sz00 )
= ( szmzizndt0 @ xS ) ),
inference(rewrite,[status(thm)],[4755,594]) ).
thf(5112,plain,
( ( ( szmzizndt0 @ xS )
= xS )
| ( ( sdtlpdtrp0 @ xN @ sz00 )
!= ( sdtlpdtrp0 @ xe @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[594,5090]) ).
thf(5144,plain,
( ( ( szmzizndt0 @ xS )
= xS )
| ( xN != xe )
| ( sz00 != sz00 ) ),
inference(simp,[status(thm)],[5112]) ).
thf(5164,plain,
( ( ( szmzizndt0 @ xS )
= xS )
| ( xN != xe ) ),
inference(simp,[status(thm)],[5144]) ).
thf(32003,plain,
( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
| ( ( aSubsetOf0 @ xS @ szNzAzT0 )
!= ( aSubsetOf0 @ xO @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,30911]) ).
thf(32058,plain,
( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
| ( xS != xO )
| ( szNzAzT0 != szNzAzT0 ) ),
inference(simp,[status(thm)],[32003]) ).
thf(32088,plain,
( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
| ( xS != xO ) ),
inference(simp,[status(thm)],[32058]) ).
thf(35062,plain,
( ( xN != xe )
| ( aElementOf0 @ xS @ xO )
| ( xS != xO )
| ( ( szmzizndt0 @ xS )
!= ( szmzizndt0 @ xO ) ) ),
inference(paramod_ordered,[status(thm)],[5164,32088]) ).
thf(35088,plain,
( ( aElementOf0 @ xS @ xO )
| ( xN != xe )
| ( xS != xO )
| ( xS != xO ) ),
inference(simp,[status(thm)],[35062]) ).
thf(35134,plain,
( ( aElementOf0 @ xS @ xO )
| ( xN != xe )
| ( xS != xO ) ),
inference(simp,[status(thm)],[35088]) ).
thf(7872,plain,
! [A: $i] :
( ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ ( slbdtrb0 @ xK ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7770,131]) ).
thf(7873,plain,
aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ xK ) ),
inference(pattern_uni,[status(thm)],[7872:[bind(A,$thf( slbdtrb0 @ xK ))]]) ).
thf(35,axiom,
( ( aFunction0 @ xd )
& ( ( szDzozmdt0 @ xd )
= szNzAzT0 )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) )
=> ( ( sdtlpdtrp0 @ xd @ A )
= ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).
thf(204,plain,
( ( aFunction0 @ xd )
& ( ( szDzozmdt0 @ xd )
= szNzAzT0 )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) )
=> ( ( sdtlpdtrp0 @ xd @ A )
= ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(206,plain,
( ( szDzozmdt0 @ xd )
= szNzAzT0 ),
inference(cnf,[status(esa)],[204]) ).
thf(209,plain,
( ( szDzozmdt0 @ xd )
= szNzAzT0 ),
inference(lifteq,[status(thm)],[206]) ).
thf(12816,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xc )
!= ( szDzozmdt0 @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[209,7368]) ).
thf(12864,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( xc != xd ) ),
inference(simp,[status(thm)],[12816]) ).
thf(12874,plain,
( ( xc != xd )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,12864]) ).
thf(12921,plain,
( ( xc != xd )
| ( ( szDzozmdt0 @ xc )
!= slcrc0 ) ),
inference(simp,[status(thm)],[12874]) ).
thf(589,plain,
( ( szDzozmdt0 @ xN )
= szNzAzT0 ),
inference(cnf,[status(esa)],[587]) ).
thf(593,plain,
( ( szDzozmdt0 @ xN )
= szNzAzT0 ),
inference(lifteq,[status(thm)],[589]) ).
thf(12800,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xN )
!= ( szDzozmdt0 @ xc ) ) ),
inference(paramod_ordered,[status(thm)],[593,7368]) ).
thf(12865,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( xN != xc ) ),
inference(simp,[status(thm)],[12800]) ).
thf(850,plain,
! [A: $i] :
( ( A = sz00 )
| ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
| ( ( aElementOf0 @ sk1 @ xO )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[101,517]) ).
thf(1165,plain,
! [A: $i] :
( ( A = sz00 )
| ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
| ( sk1 != A )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[850]) ).
thf(1175,plain,
( ( sk1 = sz00 )
| ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[1165]) ).
thf(1181,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( xO != szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1175,101]) ).
thf(1182,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( xO != szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO ) ),
inference(pattern_uni,[status(thm)],[1181:[]]) ).
thf(1343,plain,
( ( xO != szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
!= ( aElementOf0 @ sz00 @ xO ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1182]) ).
thf(1346,plain,
( ( aElementOf0 @ sz00 @ xO )
| ( xO != szNzAzT0 )
| ( ( sk31 @ sk1 )
!= sz00 )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[1343]) ).
thf(1354,plain,
( ( aElementOf0 @ sz00 @ xO )
| ( xO != szNzAzT0 )
| ( ( sk31 @ sk1 )
!= sz00 ) ),
inference(simp,[status(thm)],[1346]) ).
thf(23,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
thf(152,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aSet0 @ B )
| ~ ( isFinite0 @ B )
| ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[152]) ).
thf(75,axiom,
( ( aFunction0 @ xC )
& ( ( szDzozmdt0 @ xC )
= szNzAzT0 )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aFunction0 @ ( sdtlpdtrp0 @ xC @ A ) )
& ( ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) )
= ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) )
& ! [B: $i] :
( ( ( aSet0 @ B )
& ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) )
=> ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B )
= ( sdtlpdtrp0 @ xc @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4151) ).
thf(446,plain,
( ( aFunction0 @ xC )
& ( ( szDzozmdt0 @ xC )
= szNzAzT0 )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aFunction0 @ ( sdtlpdtrp0 @ xC @ A ) )
& ( ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) )
= ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) )
& ! [B: $i] :
( ( ( aSet0 @ B )
& ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) )
=> ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B )
= ( sdtlpdtrp0 @ xc @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(447,plain,
( ( szDzozmdt0 @ xC )
= szNzAzT0 ),
inference(cnf,[status(esa)],[446]) ).
thf(454,plain,
( ( szDzozmdt0 @ xC )
= szNzAzT0 ),
inference(lifteq,[status(thm)],[447]) ).
thf(1667,plain,
! [A: $i] :
( ( aSubsetOf0 @ A @ A )
| ( ( aSet0 @ ( szDzozmdt0 @ xc ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1251,135]) ).
thf(1668,plain,
aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ ( szDzozmdt0 @ xc ),
inference(pattern_uni,[status(thm)],[1667:[bind(A,$thf( szDzozmdt0 @ xc ))]]) ).
thf(1740,plain,
( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xC )
!= ( szDzozmdt0 @ xc ) ) ),
inference(paramod_ordered,[status(thm)],[454,1668]) ).
thf(1746,plain,
( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
| ( xC != xc ) ),
inference(simp,[status(thm)],[1740]) ).
thf(34038,plain,
! [A: $i] :
( ( aSubsetOf0 @ A @ A )
| ( ( aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31912,135]) ).
thf(34039,plain,
aSubsetOf0 @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ) @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ),
inference(pattern_uni,[status(thm)],[34038:[bind(A,$thf( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ))]]) ).
thf(50,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ? [B: $i] :
( ( aElementOf0 @ B @ xT )
& ! [C: $i] :
( ( ( aSet0 @ C )
& ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) )
=> ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4618) ).
thf(258,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ? [B: $i] :
( ( aElementOf0 @ B @ xT )
& ! [C: $i] :
( ( ( aSet0 @ C )
& ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) )
=> ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(259,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( aElementOf0 @ ( sk7 @ A ) @ xT ) ),
inference(cnf,[status(esa)],[258]) ).
thf(39683,plain,
! [A: $i] :
( ( aElementOf0 @ ( sk7 @ A ) @ xT )
| ( ( aElementOf0 @ xk @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[508,259]) ).
thf(39684,plain,
aElementOf0 @ ( sk7 @ xk ) @ xT,
inference(pattern_uni,[status(thm)],[39683:[bind(A,$thf( xk ))]]) ).
thf(46,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).
thf(237,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElementOf0 @ B @ A )
| ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
= A ) ),
inference(cnf,[status(esa)],[237]) ).
thf(239,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
= A )
| ~ ( aSet0 @ A )
| ~ ( aElementOf0 @ B @ A ) ),
inference(lifteq,[status(thm)],[238]) ).
thf(26090,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
= A )
| ~ ( aSet0 @ A )
| ( ( aElementOf0 @ sk1 @ xO )
!= ( aElementOf0 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,239]) ).
thf(26091,plain,
( ( ( sdtpldt0 @ ( sdtmndt0 @ xO @ sk1 ) @ sk1 )
= xO )
| ~ ( aSet0 @ xO ) ),
inference(pattern_uni,[status(thm)],[26090:[bind(A,$thf( xO )),bind(B,$thf( sk1 ))]]) ).
thf(68751,plain,
( ( ( sdtpldt0 @ ( sdtmndt0 @ xO @ sk1 ) @ sk1 )
= xO )
| ~ $true ),
inference(rewrite,[status(thm)],[26091,199]) ).
thf(68752,plain,
( ( sdtpldt0 @ ( sdtmndt0 @ xO @ sk1 ) @ sk1 )
= xO ),
inference(simp,[status(thm)],[68751]) ).
thf(66,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
thf(417,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ( C
!= ( sdtmndt0 @ A @ B ) )
| ~ ( aElementOf0 @ D @ C )
| ( aElementOf0 @ D @ A ) ),
inference(cnf,[status(esa)],[263]) ).
thf(287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElementOf0 @ D @ C )
| ( aElementOf0 @ D @ A ) ),
inference(lifteq,[status(thm)],[272]) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElementOf0 @ C @ ( sdtmndt0 @ A @ B ) )
| ( aElementOf0 @ C @ A ) ),
inference(simp,[status(thm)],[287]) ).
thf(19068,plain,
! [A: $i] :
( ( xk = sz00 )
| ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
| ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[873,217]) ).
thf(19069,plain,
( ( xk = sz00 )
| ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xk ) ) @ szNzAzT0 ) ),
inference(pattern_uni,[status(thm)],[19068:[bind(A,$thf( sk31 @ xk ))]]) ).
thf(1264,plain,
! [A: $i] :
( ( ( sbrdtbr0 @ A )
!= sz00 )
| ( A = slcrc0 )
| ( ( aSet0 @ ( szDzozmdt0 @ xc ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1251,108]) ).
thf(1265,plain,
( ( ( sbrdtbr0 @ ( szDzozmdt0 @ xc ) )
!= sz00 )
| ( ( szDzozmdt0 @ xc )
= slcrc0 ) ),
inference(pattern_uni,[status(thm)],[1264:[bind(A,$thf( szDzozmdt0 @ xc ))]]) ).
thf(32209,plain,
! [A: $i] :
( ( xO != szNzAzT0 )
| ( aSet0 @ ( slbdtrb0 @ A ) )
| ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[32083,186]) ).
thf(32261,plain,
! [A: $i] :
( ( aSet0 @ ( slbdtrb0 @ A ) )
| ( xO != szNzAzT0 )
| ( ( szmzizndt0 @ xO )
!= A )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[32209]) ).
thf(32270,plain,
( ( aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ xO ) ) )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[32261]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 )
& ( A != B ) )
=> ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3821) ).
thf(255,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 )
& ( A != B ) )
=> ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ szNzAzT0 )
| ( A = B )
| ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ B ) ) ) ),
inference(cnf,[status(esa)],[255]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ B ) ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ szNzAzT0 ) ),
inference(lifteq,[status(thm)],[256]) ).
thf(55,axiom,
( ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
& ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4854) ).
thf(319,plain,
( ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
& ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(320,plain,
isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ),
inference(cnf,[status(esa)],[319]) ).
thf(8024,plain,
! [A: $i] :
( ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xK ) ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7773,131]) ).
thf(8025,plain,
aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ ( sk31 @ xK ) ) ),
inference(pattern_uni,[status(thm)],[8024:[bind(A,$thf( slbdtrb0 @ ( sk31 @ xK ) ))]]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ~ ( aElementOf0 @ ( sk3 @ B @ A ) @ szNzAzT0 )
| ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ ( sk3 @ B @ A ) ) @ A )
| ~ ( sk2 @ A @ B )
| ( B
= ( slbdtrb0 @ A ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( B
= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ~ ( aElementOf0 @ ( sk3 @ B @ A ) @ szNzAzT0 )
| ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ ( sk3 @ B @ A ) ) @ A )
| ~ ( sk2 @ A @ B ) ),
inference(lifteq,[status(thm)],[173]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( B
= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ~ ( aElementOf0 @ ( sk3 @ B @ A ) @ szNzAzT0 )
| ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ ( sk3 @ B @ A ) ) @ A )
| ~ ( sk2 @ A @ B ) ),
inference(simp,[status(thm)],[183]) ).
thf(20058,plain,
! [A: $i] :
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
| ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[1560,218]) ).
thf(20059,plain,
isCountable0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) ),
inference(pattern_uni,[status(thm)],[20058:[bind(A,$thf( sk31 @ xK ))]]) ).
thf(4335,plain,
( ~ ( isFinite0 @ xS )
| ( ( aSet0 @ xS )
!= ( aSet0 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[363,4286]) ).
thf(4349,plain,
( ~ ( isFinite0 @ xS )
| ( xS != szNzAzT0 ) ),
inference(simp,[status(thm)],[4335]) ).
thf(24541,plain,
( ( xO != szNzAzT0 )
| ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
| ( ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,8213]) ).
thf(24558,plain,
( ( xO != szNzAzT0 )
| ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
| ( ( slbdtrb0 @ sk1 )
!= xT ) ),
inference(simp,[status(thm)],[24541]) ).
thf(178,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( B
!= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ C @ B )
| ( aElementOf0 @ C @ szNzAzT0 ) ),
inference(cnf,[status(esa)],[169]) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ C @ B )
| ( aElementOf0 @ C @ szNzAzT0 ) ),
inference(lifteq,[status(thm)],[178]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ ( slbdtrb0 @ A ) )
| ( aElementOf0 @ B @ szNzAzT0 ) ),
inference(simp,[status(thm)],[195]) ).
thf(26,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCDiffSet) ).
thf(156,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aSet0 @ B )
| ~ ( isCountable0 @ B )
| ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(32193,plain,
! [A: $i] :
( ( xO != szNzAzT0 )
| ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
| ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[32083,218]) ).
thf(32225,plain,
! [A: $i] :
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
| ( xO != szNzAzT0 )
| ( ( szmzizndt0 @ xO )
!= A )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[32193]) ).
thf(32288,plain,
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ xO ) ) )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[32225]) ).
thf(38229,plain,
( ( xO != szNzAzT0 )
| ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ xO ) ) )
!= ( isCountable0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[32288,4360]) ).
thf(38320,plain,
( ( xO != szNzAzT0 )
| ( ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ xO ) )
!= xT ) ),
inference(simp,[status(thm)],[38229]) ).
thf(7941,plain,
( ~ ( isFinite0 @ xS )
| ( ( aSet0 @ ( slbdtrb0 @ xk ) )
!= ( aSet0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[7779,4286]) ).
thf(7945,plain,
( ~ ( isFinite0 @ xS )
| ( ( slbdtrb0 @ xk )
!= xS ) ),
inference(simp,[status(thm)],[7941]) ).
thf(7307,plain,
( ~ ( isCountable0 @ ( szDzozmdt0 @ xc ) )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,4298]) ).
thf(7372,plain,
( ~ ( isCountable0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xc )
!= slcrc0 ) ),
inference(simp,[status(thm)],[7307]) ).
thf(18243,plain,
( ( ( szDzozmdt0 @ xc )
!= slcrc0 )
| ( ( isCountable0 @ ( szDzozmdt0 @ xc ) )
!= ( isCountable0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[456,7372]) ).
thf(18333,plain,
( ( ( szDzozmdt0 @ xc )
!= slcrc0 )
| ( ( szDzozmdt0 @ xc )
!= xS ) ),
inference(simp,[status(thm)],[18243]) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ( C
!= ( sdtmndt0 @ A @ B ) )
| ~ ( aElementOf0 @ D @ C )
| ( D != B ) ),
inference(cnf,[status(esa)],[263]) ).
thf(283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( sdtmndt0 @ A @ B ) )
| ( D != B )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElementOf0 @ D @ C ) ),
inference(lifteq,[status(thm)],[264]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElementOf0 @ B @ ( sdtmndt0 @ A @ B ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(42,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgRng) ).
thf(227,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ~ ( aFunction0 @ A )
| ~ ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) ),
inference(cnf,[status(esa)],[227]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
<=> ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ ( szszuzczcdt0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).
thf(316,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
=> ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ ( szszuzczcdt0 @ B ) ) )
& ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ ( szszuzczcdt0 @ B ) )
=> ( sdtlseqdt0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ~ ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) )
| ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B )
= ( sk7 @ A ) ) ),
inference(cnf,[status(esa)],[258]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B )
= ( sk7 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ~ ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) ),
inference(lifteq,[status(thm)],[260]) ).
thf(1358,plain,
! [A: $i] :
( ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ slcrc0 )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[372,131]) ).
thf(1359,plain,
aElement0 @ ( sbrdtbr0 @ slcrc0 ),
inference(pattern_uni,[status(thm)],[1358:[bind(A,$thf( slcrc0 ))]]) ).
thf(107,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ( A != slcrc0 )
| ( ( sbrdtbr0 @ A )
= sz00 ) ),
inference(cnf,[status(esa)],[105]) ).
thf(109,plain,
! [A: $i] :
( ( A != slcrc0 )
| ( ( sbrdtbr0 @ A )
= sz00 )
| ~ ( aSet0 @ A ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(110,plain,
( ( ( sbrdtbr0 @ slcrc0 )
= sz00 )
| ~ ( aSet0 @ slcrc0 ) ),
inference(simp,[status(thm)],[109]) ).
thf(690,plain,
( ( ( sbrdtbr0 @ slcrc0 )
= sz00 )
| ~ $true ),
inference(rewrite,[status(thm)],[110,372]) ).
thf(691,plain,
( ( sbrdtbr0 @ slcrc0 )
= sz00 ),
inference(simp,[status(thm)],[690]) ).
thf(1379,plain,
aElement0 @ sz00,
inference(rewrite,[status(thm)],[1359,691]) ).
thf(39710,plain,
! [A: $i] :
( ( aElementOf0 @ ( sk7 @ A ) @ xT )
| ( ( aElementOf0 @ sz00 @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[240,259]) ).
thf(39711,plain,
aElementOf0 @ ( sk7 @ sz00 ) @ xT,
inference(pattern_uni,[status(thm)],[39710:[bind(A,$thf( sz00 ))]]) ).
thf(67,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) )
=> ( aElementOf0 @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ ( slbdtsldtrb0 @ xS @ xK ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3965) ).
thf(421,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) )
=> ( aElementOf0 @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ ( slbdtsldtrb0 @ xS @ xK ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(20692,plain,
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) ) )
!= ( isCountable0 @ slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[20059,647]) ).
thf(20772,plain,
( ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) )
!= slcrc0 ),
inference(simp,[status(thm)],[20692]) ).
thf(20842,plain,
( ( xO != szNzAzT0 )
| ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ sk1 ) )
!= ( isCountable0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[20194,4360]) ).
thf(20890,plain,
( ( xO != szNzAzT0 )
| ( ( sdtlpdtrp0 @ xN @ sk1 )
!= xT ) ),
inference(simp,[status(thm)],[20842]) ).
thf(7785,plain,
! [A: $i] :
( ( sk1 = sz00 )
| ( xO != szNzAzT0 )
| ( aSet0 @ ( slbdtrb0 @ A ) )
| ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[1175,186]) ).
thf(7786,plain,
( ( sk1 = sz00 )
| ( xO != szNzAzT0 )
| ( aSet0 @ ( slbdtrb0 @ ( sk31 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7785:[bind(A,$thf( sk31 @ sk1 ))]]) ).
thf(1663,plain,
! [A: $i] :
( ( aSubsetOf0 @ A @ A )
| ( ( aSet0 @ xT )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,135]) ).
thf(1664,plain,
aSubsetOf0 @ xT @ xT,
inference(pattern_uni,[status(thm)],[1663:[bind(A,$thf( xT ))]]) ).
thf(38203,plain,
( ( xO != szNzAzT0 )
| ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ xO ) ) )
!= ( isCountable0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[32288,647]) ).
thf(38307,plain,
( ( xO != szNzAzT0 )
| ( ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ xO ) )
!= slcrc0 ) ),
inference(simp,[status(thm)],[38203]) ).
thf(591,plain,
aFunction0 @ xN,
inference(cnf,[status(esa)],[587]) ).
thf(321,plain,
aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT,
inference(cnf,[status(esa)],[319]) ).
thf(7306,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( ( isCountable0 @ ( szDzozmdt0 @ xc ) )
!= ( isCountable0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[456,4298]) ).
thf(7376,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xc )
!= xS ) ),
inference(simp,[status(thm)],[7306]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( aElementOf0 @ A @ ( slbdtrb0 @ ( szszuzczcdt0 @ B ) ) )
<=> ( ( aElementOf0 @ A @ ( slbdtrb0 @ B ) )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegSucc) ).
thf(574,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( aElementOf0 @ A @ ( slbdtrb0 @ ( szszuzczcdt0 @ B ) ) )
=> ( ( aElementOf0 @ A @ ( slbdtrb0 @ B ) )
| ( A = B ) ) )
& ( ( ( aElementOf0 @ A @ ( slbdtrb0 @ B ) )
| ( A = B ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ ( szszuzczcdt0 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(19112,plain,
! [A: $i] :
( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
| ( ( aElementOf0 @ xk @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[508,217]) ).
thf(19113,plain,
aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ xk ) @ szNzAzT0,
inference(pattern_uni,[status(thm)],[19112:[bind(A,$thf( xk ))]]) ).
thf(7356,plain,
( ~ ( isCountable0 @ ( szDzozmdt0 @ xc ) )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,4298]) ).
thf(7374,plain,
( ~ ( isCountable0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xc )
!= xT ) ),
inference(simp,[status(thm)],[7356]) ).
thf(18706,plain,
( ( ( szDzozmdt0 @ xc )
!= xT )
| ( ( isCountable0 @ ( szDzozmdt0 @ xc ) )
!= ( isCountable0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[456,7374]) ).
thf(18786,plain,
( ( ( szDzozmdt0 @ xc )
!= xT )
| ( ( szDzozmdt0 @ xc )
!= xS ) ),
inference(simp,[status(thm)],[18706]) ).
thf(164,plain,
( ( szDzozmdt0 @ xe )
= szNzAzT0 ),
inference(cnf,[status(esa)],[162]) ).
thf(167,plain,
( ( szDzozmdt0 @ xe )
= szNzAzT0 ),
inference(lifteq,[status(thm)],[164]) ).
thf(117,plain,
aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) @ xT,
inference(cnf,[status(esa)],[116]) ).
thf(817,plain,
( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
| ( ( szDzozmdt0 @ xc )
!= ( szDzozmdt0 @ xe ) ) ),
inference(paramod_ordered,[status(thm)],[167,117]) ).
thf(821,plain,
( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
| ( xc != xe ) ),
inference(simp,[status(thm)],[817]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRel) ).
thf(602,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(270,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( sk8 @ A @ B @ C )
| ( ( sk10 @ C @ B @ A )
!= B )
| ( C
= ( sdtmndt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[263]) ).
thf(279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk10 @ C @ B @ A )
!= B )
| ( C
= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( sk8 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[270]) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk10 @ C @ B @ A )
!= B )
| ( C
= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( sk8 @ A @ B @ C ) ),
inference(simp,[status(thm)],[279]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( isFinite0 @ A )
& ( sdtlseqdt0 @ B @ ( sbrdtbr0 @ A ) ) )
=> ? [C: $i] :
( ( aSubsetOf0 @ C @ A )
& ( ( sbrdtbr0 @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSubEx) ).
thf(221,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( isFinite0 @ A )
& ( sdtlseqdt0 @ B @ ( sbrdtbr0 @ A ) ) )
=> ? [C: $i] :
( ( aSubsetOf0 @ C @ A )
& ( ( sbrdtbr0 @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(198,plain,
isCountable0 @ xO,
inference(cnf,[status(esa)],[197]) ).
thf(19681,plain,
( ~ ( isFinite0 @ ( slbdtrb0 @ xK ) )
| ( ( isCountable0 @ ( slbdtrb0 @ xK ) )
!= ( isCountable0 @ xO ) ) ),
inference(paramod_ordered,[status(thm)],[198,7840]) ).
thf(19733,plain,
( ~ ( isFinite0 @ ( slbdtrb0 @ xK ) )
| ( ( slbdtrb0 @ xK )
!= xO ) ),
inference(simp,[status(thm)],[19681]) ).
thf(29008,plain,
( ( ( slbdtrb0 @ xK )
!= xO )
| ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,19733]) ).
thf(29118,plain,
( ( ( slbdtrb0 @ xK )
!= xO )
| ( ( slbdtrb0 @ xK )
!= slcrc0 ) ),
inference(simp,[status(thm)],[29008]) ).
thf(14,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( isFinite0 @ A )
& ( aSubsetOf0 @ B @ A ) )
=> ( sdtlseqdt0 @ ( sbrdtbr0 @ B ) @ ( sbrdtbr0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSub) ).
thf(132,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( isFinite0 @ A )
& ( aSubsetOf0 @ B @ A ) )
=> ( sdtlseqdt0 @ ( sbrdtbr0 @ B ) @ ( sbrdtbr0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7909,plain,
! [A: $i] :
( ~ ( isCountable0 @ A )
| ~ ( isFinite0 @ A )
| ( ( aSet0 @ ( slbdtrb0 @ xk ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7779,159]) ).
thf(7910,plain,
( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
| ~ ( isFinite0 @ ( slbdtrb0 @ xk ) ) ),
inference(pattern_uni,[status(thm)],[7909:[bind(A,$thf( slbdtrb0 @ xk ))]]) ).
thf(19768,plain,
( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
| ( ( isFinite0 @ ( slbdtrb0 @ xk ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,7910]) ).
thf(19879,plain,
( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
| ( ( slbdtrb0 @ xk )
!= slcrc0 ) ),
inference(simp,[status(thm)],[19768]) ).
thf(42270,plain,
( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
| ( ( slbdtrb0 @ xk )
!= ( slbdtrb0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[137,19879]) ).
thf(42399,plain,
( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
| ( xk != sz00 ) ),
inference(simp,[status(thm)],[42270]) ).
thf(69,axiom,
( ( aSet0 @ xO )
& ( xO
= ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).
thf(425,plain,
( ( aSet0 @ xO )
& ( xO
= ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(426,plain,
( xO
= ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
inference(cnf,[status(esa)],[425]) ).
thf(428,plain,
( ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
= xO ),
inference(lifteq,[status(thm)],[426]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isFinite0 @ A )
| ~ ( aSubsetOf0 @ B @ A )
| ( sdtlseqdt0 @ ( sbrdtbr0 @ B ) @ ( sbrdtbr0 @ A ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(52,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ! [C: $i] :
( ( C
= ( sdtexdt0 @ A @ B ) )
<=> ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= B )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefRst) ).
thf(297,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ! [C: $i] :
( ( ( C
= ( sdtexdt0 @ A @ B ) )
=> ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= B )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) ) ) ) )
& ( ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= B )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) ) ) )
=> ( C
= ( sdtexdt0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(298,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( ! [C: $i] :
( ( C
= ( sdtexdt0 @ A @ B ) )
=> ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= B )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) ) ) ) )
& ! [C: $i] :
( ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= B )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) ) ) )
=> ( C
= ( sdtexdt0 @ A @ B ) ) ) ) ) ),
inference(miniscope,[status(thm)],[297]) ).
thf(302,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
| ~ ( aFunction0 @ C )
| ( ( szDzozmdt0 @ C )
!= B )
| ( ( sdtlpdtrp0 @ C @ ( sk11 @ C @ B @ A ) )
!= ( sdtlpdtrp0 @ A @ ( sk11 @ C @ B @ A ) ) )
| ( C
= ( sdtexdt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[298]) ).
thf(306,plain,
! [C: $i,B: $i,A: $i] :
( ( ( szDzozmdt0 @ C )
!= B )
| ( ( sdtlpdtrp0 @ C @ ( sk11 @ C @ B @ A ) )
!= ( sdtlpdtrp0 @ A @ ( sk11 @ C @ B @ A ) ) )
| ( C
= ( sdtexdt0 @ A @ B ) )
| ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
| ~ ( aFunction0 @ C ) ),
inference(lifteq,[status(thm)],[302]) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( ( sdtlpdtrp0 @ B @ ( sk11 @ B @ ( szDzozmdt0 @ B ) @ A ) )
!= ( sdtlpdtrp0 @ A @ ( sk11 @ B @ ( szDzozmdt0 @ B ) @ A ) ) )
| ( ( sdtexdt0 @ A @ ( szDzozmdt0 @ B ) )
= B )
| ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ ( szDzozmdt0 @ B ) @ ( szDzozmdt0 @ A ) )
| ~ ( aFunction0 @ B ) ),
inference(simp,[status(thm)],[306]) ).
thf(268,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( sk8 @ A @ B @ C )
| ( aElementOf0 @ ( sk10 @ C @ B @ A ) @ A )
| ( C
= ( sdtmndt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[263]) ).
thf(291,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( sk8 @ A @ B @ C )
| ( aElementOf0 @ ( sk10 @ C @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[268]) ).
thf(292,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( sk8 @ A @ B @ C )
| ( aElementOf0 @ ( sk10 @ C @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[291]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ( A = slcrc0 )
| ( B
!= ( szmzizndt0 @ A ) )
| ~ ( aElementOf0 @ C @ A )
| ( sdtlseqdt0 @ B @ C ) ),
inference(cnf,[status(esa)],[242]) ).
thf(247,plain,
! [C: $i,B: $i,A: $i] :
( ( A = slcrc0 )
| ( B
!= ( szmzizndt0 @ A ) )
| ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ C @ A )
| ( sdtlseqdt0 @ B @ C ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( A = slcrc0 )
| ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ A )
| ( sdtlseqdt0 @ ( szmzizndt0 @ A ) @ B ) ),
inference(simp,[status(thm)],[247]) ).
thf(72,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSeg) ).
thf(439,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(20083,plain,
! [A: $i] :
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
| ( ( aElementOf0 @ xk @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[508,218]) ).
thf(20084,plain,
isCountable0 @ ( sdtlpdtrp0 @ xN @ xk ),
inference(pattern_uni,[status(thm)],[20083:[bind(A,$thf( xk ))]]) ).
thf(39649,plain,
! [A: $i] :
( ( aElementOf0 @ ( sk7 @ A ) @ xT )
| ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[1560,259]) ).
thf(39650,plain,
aElementOf0 @ ( sk7 @ ( sk31 @ xK ) ) @ xT,
inference(pattern_uni,[status(thm)],[39649:[bind(A,$thf( sk31 @ xK ))]]) ).
thf(59307,plain,
( ( xO != szNzAzT0 )
| ( sk1 != sz00 )
| ( ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
!= ( isCountable0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[456,59208]) ).
thf(59415,plain,
( ( xO != szNzAzT0 )
| ( sk1 != sz00 )
| ( ( slbdtrb0 @ sk1 )
!= xS ) ),
inference(simp,[status(thm)],[59307]) ).
thf(12914,plain,
( ( xc != xd )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,12864]) ).
thf(12927,plain,
( ( xc != xd )
| ( ( szDzozmdt0 @ xc )
!= xT ) ),
inference(simp,[status(thm)],[12914]) ).
thf(39,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelFSet) ).
thf(219,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(220,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isFinite0 @ A )
| ~ ( aElementOf0 @ B @ szNzAzT0 )
| ( isFinite0 @ ( slbdtsldtrb0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[219]) ).
thf(686,plain,
( ( ( sdtlpdtrp0 @ xe @ sz00 )
!= sk1 )
| ( ( aElementOf0 @ sz00 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
!= ( aElementOf0 @ sz00 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[240,673]) ).
thf(688,plain,
( ( ( sdtlpdtrp0 @ xe @ sz00 )
!= sk1 )
| ( sz00 != sz00 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[686]) ).
thf(689,plain,
( ( ( sdtlpdtrp0 @ xe @ sz00 )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[688]) ).
thf(783,plain,
( ( sk1 != xS )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= szNzAzT0 )
| ( ( sdtlpdtrp0 @ xN @ sz00 )
!= ( sdtlpdtrp0 @ xe @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[594,689]) ).
thf(792,plain,
( ( sk1 != xS )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= szNzAzT0 )
| ( xN != xe )
| ( sz00 != sz00 ) ),
inference(simp,[status(thm)],[783]) ).
thf(798,plain,
( ( sk1 != xS )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= szNzAzT0 )
| ( xN != xe ) ),
inference(simp,[status(thm)],[792]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aElement0 @ B ) )
=> ( aSubsetOf0 @ ( sdtlbdtrb0 @ A @ B ) @ ( szDzozmdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPttSet) ).
thf(200,plain,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aElement0 @ B ) )
=> ( aSubsetOf0 @ ( sdtlbdtrb0 @ A @ B ) @ ( szDzozmdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ~ ( aFunction0 @ A )
| ~ ( aElement0 @ B )
| ( aSubsetOf0 @ ( sdtlbdtrb0 @ A @ B ) @ ( szDzozmdt0 @ A ) ) ),
inference(cnf,[status(esa)],[200]) ).
thf(13096,plain,
( ( xN != xc )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,12865]) ).
thf(13104,plain,
( ( xN != xc )
| ( ( szDzozmdt0 @ xc )
!= xT ) ),
inference(simp,[status(thm)],[13096]) ).
thf(4301,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isFinite0 @ A )
| ( ( isCountable0 @ szNzAzT0 )
!= ( isCountable0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[362,159]) ).
thf(4302,plain,
( ~ ( aSet0 @ szNzAzT0 )
| ~ ( isFinite0 @ szNzAzT0 ) ),
inference(pattern_uni,[status(thm)],[4301:[bind(A,$thf( szNzAzT0 ))]]) ).
thf(4556,plain,
( ~ $true
| ~ ( isFinite0 @ szNzAzT0 ) ),
inference(rewrite,[status(thm)],[4302,363]) ).
thf(4557,plain,
~ ( isFinite0 @ szNzAzT0 ),
inference(simp,[status(thm)],[4556]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubASymm) ).
thf(141,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aSet0 @ B )
| ~ ( aSubsetOf0 @ A @ B )
| ~ ( aSubsetOf0 @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[141]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( aSet0 @ A )
| ~ ( aSet0 @ B )
| ~ ( aSubsetOf0 @ A @ B )
| ~ ( aSubsetOf0 @ B @ A ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(2895,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aSet0 @ B )
| ~ ( aSubsetOf0 @ A @ B )
| ~ ( aSubsetOf0 @ B @ A )
| ( B != slcrc0 )
| ( A != xO ) ),
inference(paramod_ordered,[status(thm)],[143,607]) ).
thf(2896,plain,
! [A: $i] :
( ~ ( aSet0 @ xO )
| ~ ( aSet0 @ A )
| ~ ( aSubsetOf0 @ xO @ A )
| ~ ( aSubsetOf0 @ A @ xO )
| ( A != slcrc0 ) ),
inference(pattern_uni,[status(thm)],[2895:[bind(A,$thf( xO ))]]) ).
thf(3192,plain,
( ~ ( aSet0 @ xO )
| ~ ( aSet0 @ slcrc0 )
| ~ ( aSubsetOf0 @ xO @ slcrc0 )
| ~ ( aSubsetOf0 @ slcrc0 @ xO ) ),
inference(simp,[status(thm)],[2896]) ).
thf(4144,plain,
( ~ $true
| ~ $true
| ~ ( aSubsetOf0 @ xO @ slcrc0 )
| ~ ( aSubsetOf0 @ slcrc0 @ xO ) ),
inference(rewrite,[status(thm)],[3192,372,199]) ).
thf(4145,plain,
( ~ ( aSubsetOf0 @ xO @ slcrc0 )
| ~ ( aSubsetOf0 @ slcrc0 @ xO ) ),
inference(simp,[status(thm)],[4144]) ).
thf(4152,plain,
( ~ ( aSubsetOf0 @ slcrc0 @ xO )
| ( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ ( szDzozmdt0 @ xc ) )
!= ( aSubsetOf0 @ xO @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[1668,4145]) ).
thf(4192,plain,
( ~ ( aSubsetOf0 @ slcrc0 @ xO )
| ( ( szDzozmdt0 @ xc )
!= xO )
| ( ( szDzozmdt0 @ xc )
!= slcrc0 ) ),
inference(simp,[status(thm)],[4152]) ).
thf(7615,plain,
( ( ( szDzozmdt0 @ xc )
!= xO )
| ( ( szDzozmdt0 @ xc )
!= slcrc0 )
| ( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ ( szDzozmdt0 @ xc ) )
!= ( aSubsetOf0 @ slcrc0 @ xO ) ) ),
inference(paramod_ordered,[status(thm)],[1668,4192]) ).
thf(7677,plain,
( ( ( szDzozmdt0 @ xc )
!= xO )
| ( ( szDzozmdt0 @ xc )
!= slcrc0 )
| ( ( szDzozmdt0 @ xc )
!= slcrc0 )
| ( ( szDzozmdt0 @ xc )
!= xO ) ),
inference(simp,[status(thm)],[7615]) ).
thf(7703,plain,
( ( ( szDzozmdt0 @ xc )
!= xO )
| ( ( szDzozmdt0 @ xc )
!= slcrc0 ) ),
inference(simp,[status(thm)],[7677]) ).
thf(34836,plain,
! [A: $i] :
( ( aSet0 @ ( slbdtrb0 @ A ) )
| ( ( aElementOf0 @ ( szmzizndt0 @ xS ) @ xS )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[34726,186]) ).
thf(34853,plain,
! [A: $i] :
( ( aSet0 @ ( slbdtrb0 @ A ) )
| ( ( szmzizndt0 @ xS )
!= A )
| ( xS != szNzAzT0 ) ),
inference(simp,[status(thm)],[34836]) ).
thf(34898,plain,
( ( aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ xS ) ) )
| ( xS != szNzAzT0 ) ),
inference(simp,[status(thm)],[34853]) ).
thf(4365,plain,
( ( isCountable0 @ xT )
!= ( isCountable0 @ szNzAzT0 ) ),
inference(paramod_ordered,[status(thm)],[362,4360]) ).
thf(4375,plain,
xT != szNzAzT0,
inference(simp,[status(thm)],[4365]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( B
!= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ C @ B )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ),
inference(cnf,[status(esa)],[169]) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ C @ B )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ),
inference(lifteq,[status(thm)],[175]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ ( slbdtrb0 @ A ) )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A ) ),
inference(simp,[status(thm)],[191]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEquSucc) ).
thf(429,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(165,plain,
aFunction0 @ xe,
inference(cnf,[status(esa)],[162]) ).
thf(609,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
!= sk1 )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( ( aElementOf0 @ sk1 @ xO )
!= ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[101,102]) ).
thf(611,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
!= sk1 )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( sk1 != A )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO ) ),
inference(simp,[status(thm)],[609]) ).
thf(613,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ~ ( aElementOf0 @ sk1 @ szNzAzT0 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO ) ),
inference(simp,[status(thm)],[611]) ).
thf(720,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO )
| ( ( aElementOf0 @ sk1 @ szNzAzT0 )
!= ( aElementOf0 @ xk @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[508,613]) ).
thf(726,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO )
| ( sk1 != xk )
| ( szNzAzT0 != szNzAzT0 ) ),
inference(simp,[status(thm)],[720]) ).
thf(729,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO )
| ( sk1 != xk ) ),
inference(simp,[status(thm)],[726]) ).
thf(19081,plain,
! [A: $i] :
( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
| ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[1560,217]) ).
thf(19082,plain,
aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) ) @ szNzAzT0,
inference(pattern_uni,[status(thm)],[19081:[bind(A,$thf( sk31 @ xK ))]]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ( A = slcrc0 )
| ~ ( aElementOf0 @ B @ A )
| ( aElementOf0 @ ( sk6 @ B @ A ) @ A )
| ( B
= ( szmzizndt0 @ A ) ) ),
inference(cnf,[status(esa)],[242]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( A = slcrc0 )
| ( B
= ( szmzizndt0 @ A ) )
| ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ A )
| ( aElementOf0 @ ( sk6 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[245]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( A = slcrc0 )
| ( B
= ( szmzizndt0 @ A ) )
| ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ A )
| ( aElementOf0 @ ( sk6 @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[251]) ).
thf(19788,plain,
( ~ ( isFinite0 @ ( slbdtrb0 @ xk ) )
| ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
!= ( isCountable0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[456,7910]) ).
thf(19886,plain,
( ~ ( isFinite0 @ ( slbdtrb0 @ xk ) )
| ( ( slbdtrb0 @ xk )
!= xS ) ),
inference(simp,[status(thm)],[19788]) ).
thf(19642,plain,
( ~ ( isFinite0 @ ( slbdtrb0 @ xK ) )
| ( ( isCountable0 @ ( slbdtrb0 @ xK ) )
!= ( isCountable0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[456,7840]) ).
thf(19731,plain,
( ~ ( isFinite0 @ ( slbdtrb0 @ xK ) )
| ( ( slbdtrb0 @ xK )
!= xS ) ),
inference(simp,[status(thm)],[19642]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElementOf0 @ B @ szNzAzT0 )
| ~ ( isFinite0 @ A )
| ~ ( sdtlseqdt0 @ B @ ( sbrdtbr0 @ A ) )
| ( ( sbrdtbr0 @ ( sk5 @ B @ A ) )
= B ) ),
inference(cnf,[status(esa)],[221]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( ( sbrdtbr0 @ ( sk5 @ B @ A ) )
= B )
| ~ ( aSet0 @ A )
| ~ ( aElementOf0 @ B @ szNzAzT0 )
| ~ ( isFinite0 @ A )
| ~ ( sdtlseqdt0 @ B @ ( sbrdtbr0 @ A ) ) ),
inference(lifteq,[status(thm)],[222]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aSet0 @ B ) )
=> ( ~ ( aElementOf0 @ A @ B )
=> ( ( sdtmndt0 @ ( sdtpldt0 @ B @ A ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).
thf(229,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aSet0 @ B ) )
=> ( ~ ( aElementOf0 @ A @ B )
=> ( ( sdtmndt0 @ ( sdtpldt0 @ B @ A ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(8251,plain,
( ( xO != szNzAzT0 )
| ~ ( isFinite0 @ xS )
| ( ( aSet0 @ ( slbdtrb0 @ sk1 ) )
!= ( aSet0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[7814,4286]) ).
thf(8255,plain,
( ( xO != szNzAzT0 )
| ~ ( isFinite0 @ xS )
| ( ( slbdtrb0 @ sk1 )
!= xS ) ),
inference(simp,[status(thm)],[8251]) ).
thf(88,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i,C: $i] :
( ( ( aSet0 @ B )
& ( aSet0 @ C )
& ( A != sz00 ) )
=> ( ( ( aSubsetOf0 @ ( slbdtsldtrb0 @ B @ A ) @ ( slbdtsldtrb0 @ C @ A ) )
& ( ( slbdtsldtrb0 @ B @ A )
!= slcrc0 ) )
=> ( aSubsetOf0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelSub) ).
thf(566,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i,C: $i] :
( ( ( aSet0 @ B )
& ( aSet0 @ C )
& ( A != sz00 ) )
=> ( ( ( aSubsetOf0 @ ( slbdtsldtrb0 @ B @ A ) @ ( slbdtsldtrb0 @ C @ A ) )
& ( ( slbdtsldtrb0 @ B @ A )
!= slcrc0 ) )
=> ( aSubsetOf0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(20046,plain,
! [A: $i] :
( ( xk = sz00 )
| ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
| ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[873,218]) ).
thf(20047,plain,
( ( xk = sz00 )
| ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xk ) ) ) ),
inference(pattern_uni,[status(thm)],[20046:[bind(A,$thf( sk31 @ xk ))]]) ).
thf(7841,plain,
! [A: $i] :
( ( ( sbrdtbr0 @ A )
!= sz00 )
| ( A = slcrc0 )
| ( ( aSet0 @ ( slbdtrb0 @ xK ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7770,108]) ).
thf(7842,plain,
( ( ( sbrdtbr0 @ ( slbdtrb0 @ xK ) )
!= sz00 )
| ( ( slbdtrb0 @ xK )
= slcrc0 ) ),
inference(pattern_uni,[status(thm)],[7841:[bind(A,$thf( slbdtrb0 @ xK ))]]) ).
thf(2055,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aSet0 @ B )
| ~ ( aSubsetOf0 @ A @ B )
| ~ ( aSubsetOf0 @ B @ A )
| ( B != slcrc0 )
| ( A != xS ) ),
inference(paramod_ordered,[status(thm)],[143,660]) ).
thf(2056,plain,
! [A: $i] :
( ~ ( aSet0 @ xS )
| ~ ( aSet0 @ A )
| ~ ( aSubsetOf0 @ xS @ A )
| ~ ( aSubsetOf0 @ A @ xS )
| ( A != slcrc0 ) ),
inference(pattern_uni,[status(thm)],[2055:[bind(A,$thf( xS ))]]) ).
thf(2929,plain,
( ~ ( aSet0 @ xS )
| ~ ( aSet0 @ slcrc0 )
| ~ ( aSubsetOf0 @ xS @ slcrc0 )
| ~ ( aSubsetOf0 @ slcrc0 @ xS ) ),
inference(simp,[status(thm)],[2056]) ).
thf(3253,plain,
( ~ ( aSet0 @ xS )
| ~ $true
| ~ ( aSubsetOf0 @ xS @ slcrc0 )
| ~ ( aSubsetOf0 @ slcrc0 @ xS ) ),
inference(rewrite,[status(thm)],[2929,372]) ).
thf(3254,plain,
( ~ ( aSet0 @ xS )
| ~ ( aSubsetOf0 @ xS @ slcrc0 )
| ~ ( aSubsetOf0 @ slcrc0 @ xS ) ),
inference(simp,[status(thm)],[3253]) ).
thf(65,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ! [C: $i] :
( ( C
= ( sdtlcdtrc0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSImg) ).
thf(388,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ! [C: $i] :
( ( ( C
= ( sdtlcdtrc0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) ) )
& ( ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) ) )
& ( ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtlcdtrc0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(12814,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xc )
!= ( szDzozmdt0 @ xe ) ) ),
inference(paramod_ordered,[status(thm)],[167,7368]) ).
thf(12867,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( xc != xe ) ),
inference(simp,[status(thm)],[12814]) ).
thf(13116,plain,
( ( xc != xe )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,12867]) ).
thf(13163,plain,
( ( xc != xe )
| ( ( szDzozmdt0 @ xc )
!= slcrc0 ) ),
inference(simp,[status(thm)],[13116]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ( sk2 @ A @ B )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ ( sk4 @ B @ A ) ) @ A )
| ( B
= ( slbdtrb0 @ A ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( B
= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ( sk2 @ A @ B )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ ( sk4 @ B @ A ) ) @ A ) ),
inference(lifteq,[status(thm)],[172]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( B
= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ( sk2 @ A @ B )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ ( sk4 @ B @ A ) ) @ A ) ),
inference(simp,[status(thm)],[187]) ).
thf(1360,plain,
! [A: $i] :
( ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ xT )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,131]) ).
thf(1361,plain,
aElement0 @ ( sbrdtbr0 @ xT ),
inference(pattern_uni,[status(thm)],[1360:[bind(A,$thf( xT ))]]) ).
thf(665,plain,
! [A: $i] :
( ( ( sbrdtbr0 @ A )
!= sz00 )
| ( A = slcrc0 )
| ( ( aSet0 @ xO )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[199,108]) ).
thf(666,plain,
( ( ( sbrdtbr0 @ xO )
!= sz00 )
| ( xO = slcrc0 ) ),
inference(pattern_uni,[status(thm)],[665:[bind(A,$thf( xO ))]]) ).
thf(3728,plain,
( ( sbrdtbr0 @ xO )
!= sz00 ),
inference(simplifyReflect,[status(thm)],[666,607]) ).
thf(79,axiom,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( isFinite0 @ A )
& ( A != slcrc0 ) )
=> ! [B: $i] :
( ( B
= ( szmzazxdt0 @ A ) )
<=> ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMax) ).
thf(489,plain,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( isFinite0 @ A )
& ( A != slcrc0 ) )
=> ! [B: $i] :
( ( ( B
= ( szmzazxdt0 @ A ) )
=> ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ C @ B ) ) ) )
& ( ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ C @ B ) ) )
=> ( B
= ( szmzazxdt0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(7326,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( ( isCountable0 @ ( szDzozmdt0 @ xc ) )
!= ( isCountable0 @ xO ) ) ),
inference(paramod_ordered,[status(thm)],[198,4298]) ).
thf(7365,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xc )
!= xO ) ),
inference(simp,[status(thm)],[7326]) ).
thf(69897,plain,
( ( xN != xe )
| ( ( isCountable0 @ ( sdtlpdtrp0 @ xe @ xK ) )
!= ( isCountable0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[69578,4360]) ).
thf(69954,plain,
( ( xN != xe )
| ( ( sdtlpdtrp0 @ xe @ xK )
!= xT ) ),
inference(simp,[status(thm)],[69897]) ).
thf(847,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[517,101]) ).
thf(848,plain,
( ~ ( aElementOf0 @ sk1 @ szNzAzT0 )
| ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO ) ),
inference(pattern_uni,[status(thm)],[847:[bind(A,$thf( sk1 ))]]) ).
thf(1598,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
!= ( aElementOf0 @ sk1 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[1560,848]) ).
thf(1643,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( ( sk31 @ xK )
!= sk1 )
| ( szNzAzT0 != szNzAzT0 ) ),
inference(simp,[status(thm)],[1598]) ).
thf(1659,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( ( sk31 @ xK )
!= sk1 ) ),
inference(simp,[status(thm)],[1643]) ).
thf(38099,plain,
! [A: $i] :
( ( xO != szNzAzT0 )
| ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ xO ) ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32270,131]) ).
thf(38100,plain,
( ( xO != szNzAzT0 )
| ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ ( szmzizndt0 @ xO ) ) ) ) ),
inference(pattern_uni,[status(thm)],[38099:[bind(A,$thf( slbdtrb0 @ ( szmzizndt0 @ xO ) ))]]) ).
thf(42500,plain,
( ( xk != sz00 )
| ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
!= ( isCountable0 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[362,42399]) ).
thf(42554,plain,
( ( xk != sz00 )
| ( ( slbdtrb0 @ xk )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[42500]) ).
thf(39631,plain,
! [A: $i] :
( ( aElementOf0 @ ( sk7 @ A ) @ xT )
| ( ( aElementOf0 @ xK @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[325,259]) ).
thf(39632,plain,
aElementOf0 @ ( sk7 @ xK ) @ xT,
inference(pattern_uni,[status(thm)],[39631:[bind(A,$thf( xK ))]]) ).
thf(23077,plain,
( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
| ( sdtlseqdt0 @ xk @ sz00 )
| ( xk != xk ) ),
inference(paramod_ordered,[status(thm)],[7766,22970]) ).
thf(23078,plain,
( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
| ( sdtlseqdt0 @ xk @ sz00 ) ),
inference(pattern_uni,[status(thm)],[23077:[]]) ).
thf(1724,plain,
( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xN )
!= ( szDzozmdt0 @ xc ) ) ),
inference(paramod_ordered,[status(thm)],[593,1668]) ).
thf(1744,plain,
( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
| ( xN != xc ) ),
inference(simp,[status(thm)],[1724]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
thf(210,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ szNzAzT0 )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[210]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ szNzAzT0 )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A ) ),
inference(lifteq,[status(thm)],[211]) ).
thf(699,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO )
| ( ( aElementOf0 @ sk1 @ szNzAzT0 )
!= ( aElementOf0 @ xK @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[325,613]) ).
thf(704,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO )
| ( sk1 != xK )
| ( szNzAzT0 != szNzAzT0 ) ),
inference(simp,[status(thm)],[699]) ).
thf(706,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO )
| ( sk1 != xK ) ),
inference(simp,[status(thm)],[704]) ).
thf(42282,plain,
( ( ( slbdtrb0 @ xk )
!= slcrc0 )
| ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
!= ( isCountable0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[456,19879]) ).
thf(42396,plain,
( ( ( slbdtrb0 @ xk )
!= slcrc0 )
| ( ( slbdtrb0 @ xk )
!= xS ) ),
inference(simp,[status(thm)],[42282]) ).
thf(12791,plain,
( ( ( szDzozmdt0 @ xc )
!= szNzAzT0 )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,7368]) ).
thf(12859,plain,
( ( ( szDzozmdt0 @ xc )
!= szNzAzT0 )
| ( ( szDzozmdt0 @ xc )
!= slcrc0 ) ),
inference(simp,[status(thm)],[12791]) ).
thf(10833,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ sz00 )
= xK )
| ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7781,131]) ).
thf(10834,plain,
( ( ( szszuzczcdt0 @ sz00 )
= xK )
| ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) ) ) ),
inference(pattern_uni,[status(thm)],[10833:[bind(A,$thf( slbdtrb0 @ ( sk31 @ xk ) ))]]) ).
thf(29102,plain,
( ( ( slbdtrb0 @ xK )
!= xO )
| ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,19733]) ).
thf(29114,plain,
( ( ( slbdtrb0 @ xK )
!= xO )
| ( ( slbdtrb0 @ xK )
!= xT ) ),
inference(simp,[status(thm)],[29102]) ).
thf(80,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( A
!= ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatNSucc) ).
thf(503,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( A
!= ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(13156,plain,
( ( xc != xe )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,12867]) ).
thf(13167,plain,
( ( xc != xe )
| ( ( szDzozmdt0 @ xc )
!= xT ) ),
inference(simp,[status(thm)],[13156]) ).
thf(89,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
thf(569,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(20255,plain,
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ xK ) )
!= ( isCountable0 @ xT ) ),
inference(paramod_ordered,[status(thm)],[20056,4360]) ).
thf(20290,plain,
( ( sdtlpdtrp0 @ xN @ xK )
!= xT ),
inference(simp,[status(thm)],[20255]) ).
thf(19827,plain,
( ~ ( isFinite0 @ ( slbdtrb0 @ xk ) )
| ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
!= ( isCountable0 @ xO ) ) ),
inference(paramod_ordered,[status(thm)],[198,7910]) ).
thf(19878,plain,
( ~ ( isFinite0 @ ( slbdtrb0 @ xk ) )
| ( ( slbdtrb0 @ xk )
!= xO ) ),
inference(simp,[status(thm)],[19827]) ).
thf(12342,plain,
( ( ( szDzozmdt0 @ xc )
!= xO )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,7365]) ).
thf(12361,plain,
( ( ( szDzozmdt0 @ xc )
!= xO )
| ( ( szDzozmdt0 @ xc )
!= xT ) ),
inference(simp,[status(thm)],[12342]) ).
thf(23085,plain,
( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
| ( sdtlseqdt0 @ xk @ sz00 )
| ( xk != xk ) ),
inference(paramod_ordered,[status(thm)],[873,22970]) ).
thf(23086,plain,
( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
| ( sdtlseqdt0 @ xk @ sz00 ) ),
inference(pattern_uni,[status(thm)],[23085:[]]) ).
thf(299,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
| ( C
!= ( sdtexdt0 @ A @ B ) )
| ( ( szDzozmdt0 @ C )
= B ) ),
inference(cnf,[status(esa)],[298]) ).
thf(310,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( sdtexdt0 @ A @ B ) )
| ( ( szDzozmdt0 @ C )
= B )
| ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) ) ),
inference(lifteq,[status(thm)],[299]) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( ( szDzozmdt0 @ ( sdtexdt0 @ A @ B ) )
= B )
| ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) ) ),
inference(simp,[status(thm)],[310]) ).
thf(815,plain,
( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
| ( ( szDzozmdt0 @ xN )
!= ( szDzozmdt0 @ xc ) ) ),
inference(paramod_ordered,[status(thm)],[593,117]) ).
thf(824,plain,
( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
| ( xN != xc ) ),
inference(simp,[status(thm)],[815]) ).
thf(21,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCConsSet) ).
thf(148,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1727,plain,
( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
| ( ( szDzozmdt0 @ xc )
!= ( szDzozmdt0 @ xe ) ) ),
inference(paramod_ordered,[status(thm)],[167,1668]) ).
thf(1747,plain,
( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
| ( xc != xe ) ),
inference(simp,[status(thm)],[1727]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ szNzAzT0 )
| ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A ) ),
inference(cnf,[status(esa)],[160]) ).
thf(74,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
thf(444,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(62,axiom,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( isFinite0 @ A ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( aSubsetOf0 @ A @ ( slbdtrb0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFinSubSeg) ).
thf(375,plain,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( isFinite0 @ A ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( aSubsetOf0 @ A @ ( slbdtrb0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(39608,plain,
! [A: $i] :
( ( aElementOf0 @ ( sk7 @ A ) @ xT )
| ( ( aElementOf0 @ sk1 @ xO )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[101,259]) ).
thf(39817,plain,
! [A: $i] :
( ( aElementOf0 @ ( sk7 @ A ) @ xT )
| ( sk1 != A )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[39608]) ).
thf(39888,plain,
( ( aElementOf0 @ ( sk7 @ sk1 ) @ xT )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[39817]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ( sk2 @ A @ B )
| ~ ( aElementOf0 @ ( sk4 @ B @ A ) @ B )
| ( B
= ( slbdtrb0 @ A ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( B
= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ( sk2 @ A @ B )
| ~ ( aElementOf0 @ ( sk4 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ( B
= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ( sk2 @ A @ B )
| ~ ( aElementOf0 @ ( sk4 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[179]) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( aElementOf0 @ ( sk9 @ C @ B @ A ) @ C )
| ~ ( sk8 @ A @ B @ C )
| ( C
= ( sdtmndt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[263]) ).
thf(295,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( aElementOf0 @ ( sk9 @ C @ B @ A ) @ C )
| ~ ( sk8 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[271]) ).
thf(296,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( aElementOf0 @ ( sk9 @ C @ B @ A ) @ C )
| ~ ( sk8 @ A @ B @ C ) ),
inference(simp,[status(thm)],[295]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aSet0 @ B )
| ~ ( isCountable0 @ B )
| ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[148]) ).
thf(93,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 )
<=> ( isFinite0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
thf(584,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 )
=> ( isFinite0 @ A ) )
& ( ( isFinite0 @ A )
=> ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(86,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ B ) )
=> ! [C: $i] :
( ( ( aSet0 @ C )
& ( aElementOf0 @ C @ ( slbdtsldtrb0 @ B @ xk ) ) )
=> ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4331) ).
thf(562,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ B ) )
=> ! [C: $i] :
( ( ( aSet0 @ C )
& ( aElementOf0 @ C @ ( slbdtsldtrb0 @ B @ xk ) ) )
=> ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ B @ A )
=> ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( sdtlpdtrp0 @ xN @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).
thf(423,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ B @ A )
=> ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( sdtlpdtrp0 @ xN @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(22944,plain,
! [A: $i] :
( ( xk = sz00 )
| ( sdtlseqdt0 @ A @ A )
| ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[873,226]) ).
thf(22945,plain,
( ( xk = sz00 )
| ( sdtlseqdt0 @ ( sk31 @ xk ) @ ( sk31 @ xk ) ) ),
inference(pattern_uni,[status(thm)],[22944:[bind(A,$thf( sk31 @ xk ))]]) ).
thf(267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( sk8 @ A @ B @ C )
| ~ ( aElementOf0 @ ( sk10 @ C @ B @ A ) @ C )
| ( C
= ( sdtmndt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[263]) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( sk8 @ A @ B @ C )
| ~ ( aElementOf0 @ ( sk10 @ C @ B @ A ) @ C ) ),
inference(lifteq,[status(thm)],[267]) ).
thf(286,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( sk8 @ A @ B @ C )
| ~ ( aElementOf0 @ ( sk10 @ C @ B @ A ) @ C ) ),
inference(simp,[status(thm)],[285]) ).
thf(825,plain,
( ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
!= ( isCountable0 @ slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[320,647]) ).
thf(826,plain,
( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= slcrc0 ),
inference(simp,[status(thm)],[825]) ).
thf(12848,plain,
( ( ( szDzozmdt0 @ xc )
!= szNzAzT0 )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,7368]) ).
thf(12862,plain,
( ( ( szDzozmdt0 @ xc )
!= szNzAzT0 )
| ( ( szDzozmdt0 @ xc )
!= xT ) ),
inference(simp,[status(thm)],[12848]) ).
thf(300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
| ( C
!= ( sdtexdt0 @ A @ B ) )
| ~ ( aElementOf0 @ D @ B )
| ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) ) ),
inference(cnf,[status(esa)],[298]) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( sdtexdt0 @ A @ B ) )
| ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) )
| ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
| ~ ( aElementOf0 @ D @ B ) ),
inference(lifteq,[status(thm)],[300]) ).
thf(313,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtlpdtrp0 @ ( sdtexdt0 @ A @ B ) @ C )
= ( sdtlpdtrp0 @ A @ C ) )
| ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
| ~ ( aElementOf0 @ C @ B ) ),
inference(simp,[status(thm)],[312]) ).
thf(19,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isFinite0 @ A )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFinRel) ).
thf(144,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(19864,plain,
( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
| ( ( isFinite0 @ ( slbdtrb0 @ xk ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,7910]) ).
thf(19881,plain,
( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
| ( ( slbdtrb0 @ xk )
!= xT ) ),
inference(simp,[status(thm)],[19864]) ).
thf(50155,plain,
( ( ( slbdtrb0 @ xk )
!= xT )
| ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
!= ( isCountable0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[456,19881]) ).
thf(50265,plain,
( ( ( slbdtrb0 @ xk )
!= xT )
| ( ( slbdtrb0 @ xk )
!= xS ) ),
inference(simp,[status(thm)],[50155]) ).
thf(7871,plain,
( ~ ( isFinite0 @ xS )
| ( ( aSet0 @ ( slbdtrb0 @ xK ) )
!= ( aSet0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[7770,4286]) ).
thf(7875,plain,
( ~ ( isFinite0 @ xS )
| ( ( slbdtrb0 @ xK )
!= xS ) ),
inference(simp,[status(thm)],[7871]) ).
thf(4303,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isFinite0 @ A )
| ( ( isCountable0 @ xO )
!= ( isCountable0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[198,159]) ).
thf(4304,plain,
( ~ ( aSet0 @ xO )
| ~ ( isFinite0 @ xO ) ),
inference(pattern_uni,[status(thm)],[4303:[bind(A,$thf( xO ))]]) ).
thf(4572,plain,
( ~ $true
| ~ ( isFinite0 @ xO ) ),
inference(rewrite,[status(thm)],[4304,199]) ).
thf(4573,plain,
~ ( isFinite0 @ xO ),
inference(simp,[status(thm)],[4572]) ).
thf(42501,plain,
( ( xk != sz00 )
| ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
!= ( isCountable0 @ xO ) ) ),
inference(paramod_ordered,[status(thm)],[198,42399]) ).
thf(42546,plain,
( ( xk != sz00 )
| ( ( slbdtrb0 @ xk )
!= xO ) ),
inference(simp,[status(thm)],[42501]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 )
& ( aElementOf0 @ C @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTrans) ).
thf(235,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 )
& ( aElementOf0 @ C @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(236,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ szNzAzT0 )
| ~ ( aElementOf0 @ C @ szNzAzT0 )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ C )
| ( sdtlseqdt0 @ A @ C ) ),
inference(cnf,[status(esa)],[235]) ).
thf(19826,plain,
( ~ ( isFinite0 @ ( slbdtrb0 @ xk ) )
| ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
!= ( isCountable0 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[362,7910]) ).
thf(19875,plain,
( ~ ( isFinite0 @ ( slbdtrb0 @ xk ) )
| ( ( slbdtrb0 @ xk )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[19826]) ).
thf(19718,plain,
( ~ ( isCountable0 @ ( slbdtrb0 @ xK ) )
| ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,7840]) ).
thf(19741,plain,
( ~ ( isCountable0 @ ( slbdtrb0 @ xK ) )
| ( ( slbdtrb0 @ xK )
!= xT ) ),
inference(simp,[status(thm)],[19718]) ).
thf(31578,plain,
( ( ( slbdtrb0 @ xk )
!= szNzAzT0 )
| ( ( isFinite0 @ ( slbdtrb0 @ xk ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,19875]) ).
thf(31590,plain,
( ( ( slbdtrb0 @ xk )
!= szNzAzT0 )
| ( ( slbdtrb0 @ xk )
!= xT ) ),
inference(simp,[status(thm)],[31578]) ).
thf(6,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(113,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(694,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
!= sk1 )
| ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( aElementOf0 @ xK @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[325,102]) ).
thf(695,plain,
( ( ( sdtlpdtrp0 @ xe @ xK )
!= sk1 )
| ~ ( aElementOf0 @ xK @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
inference(pattern_uni,[status(thm)],[694:[bind(A,$thf( xK ))]]) ).
thf(732,plain,
( ( ( sdtlpdtrp0 @ xe @ xK )
!= sk1 )
| ( ( aElementOf0 @ sk1 @ xO )
!= ( aElementOf0 @ xK @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[101,695]) ).
thf(736,plain,
( ( ( sdtlpdtrp0 @ xe @ xK )
!= sk1 )
| ( sk1 != xK )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO ) ),
inference(simp,[status(thm)],[732]) ).
thf(31896,plain,
! [A: $i] :
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
| ( ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[31786,218]) ).
thf(31897,plain,
isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) ),
inference(pattern_uni,[status(thm)],[31896:[bind(A,$thf( szmzizndt0 @ szNzAzT0 ))]]) ).
thf(663,plain,
! [A: $i] :
( ( ( sbrdtbr0 @ A )
!= sz00 )
| ( A = slcrc0 )
| ( ( aSet0 @ xT )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,108]) ).
thf(664,plain,
( ( ( sbrdtbr0 @ xT )
!= sz00 )
| ( xT = slcrc0 ) ),
inference(pattern_uni,[status(thm)],[663:[bind(A,$thf( xT ))]]) ).
thf(768,plain,
! [A: $i] :
( ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
!= ( aElementOf0 @ A @ slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[321,374]) ).
thf(776,plain,
! [A: $i] :
( ( ( szDzizrdt0 @ xd )
!= A )
| ( xT != slcrc0 ) ),
inference(simp,[status(thm)],[768]) ).
thf(781,plain,
xT != slcrc0,
inference(simp,[status(thm)],[776]) ).
thf(3710,plain,
( ( sbrdtbr0 @ xT )
!= sz00 ),
inference(simplifyReflect,[status(thm)],[664,781]) ).
thf(451,plain,
aFunction0 @ xC,
inference(cnf,[status(esa)],[446]) ).
thf(4361,plain,
( ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
!= ( isCountable0 @ xT ) ),
inference(paramod_ordered,[status(thm)],[320,4360]) ).
thf(4374,plain,
( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xT ),
inference(simp,[status(thm)],[4361]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ~ ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) )
| ( ( sdtlpdtrp0 @ xd @ A )
= ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[204]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B )
= ( sdtlpdtrp0 @ xd @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ~ ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) ),
inference(lifteq,[status(thm)],[205]) ).
thf(1570,plain,
! [A: $i] :
( ( A = sz00 )
| ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
| ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[1560,517]) ).
thf(1571,plain,
( ( ( sk31 @ xK )
= sz00 )
| ( aElementOf0 @ ( sk31 @ ( sk31 @ xK ) ) @ szNzAzT0 ) ),
inference(pattern_uni,[status(thm)],[1570:[bind(A,$thf( sk31 @ xK ))]]) ).
thf(96,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElement0 @ B )
=> ( ~ ( aElementOf0 @ B @ A )
=> ( ( sbrdtbr0 @ ( sdtpldt0 @ A @ B ) )
= ( szszuzczcdt0 @ ( sbrdtbr0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardCons) ).
thf(599,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElement0 @ B )
=> ( ~ ( aElementOf0 @ B @ A )
=> ( ( sbrdtbr0 @ ( sdtpldt0 @ A @ B ) )
= ( szszuzczcdt0 @ ( sbrdtbr0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(14126,plain,
( ( xO != szNzAzT0 )
| ( aSubsetOf0 @ slcrc0 @ ( slbdtrb0 @ sk1 ) )
| ( ( slbdtrb0 @ sk1 )
!= ( slbdtrb0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[137,8219]) ).
thf(14223,plain,
( ( aSubsetOf0 @ slcrc0 @ ( slbdtrb0 @ sk1 ) )
| ( xO != szNzAzT0 )
| ( sk1 != sz00 ) ),
inference(simp,[status(thm)],[14126]) ).
thf(3,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
thf(103,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(37,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ( ( ( isCountable0 @ ( szDzozmdt0 @ A ) )
& ( isFinite0 @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) )
=> ( ( aElement0 @ ( szDzizrdt0 @ A ) )
& ( isCountable0 @ ( sdtlbdtrb0 @ A @ ( szDzizrdt0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDirichlet) ).
thf(213,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ( ( ( isCountable0 @ ( szDzozmdt0 @ A ) )
& ( isFinite0 @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) )
=> ( ( aElement0 @ ( szDzizrdt0 @ A ) )
& ( isCountable0 @ ( sdtlbdtrb0 @ A @ ( szDzizrdt0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(7942,plain,
! [A: $i] :
( ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ ( slbdtrb0 @ xk ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7779,131]) ).
thf(7943,plain,
aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ xk ) ),
inference(pattern_uni,[status(thm)],[7942:[bind(A,$thf( slbdtrb0 @ xk ))]]) ).
thf(9121,plain,
( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
| ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ sz00 ) ) )
| ( xk != xk ) ),
inference(paramod_ordered,[status(thm)],[873,7943]) ).
thf(9122,plain,
( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
| ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[9121:[]]) ).
thf(18912,plain,
( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
| ( aElement0 @ ( sbrdtbr0 @ slcrc0 ) ) ),
inference(rewrite,[status(thm)],[9122,137]) ).
thf(25,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFunSort) ).
thf(155,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(827,plain,
aSubsetOf0 @ ( sdtlcdtrc0 @ xd @ szNzAzT0 ) @ xT,
inference(rewrite,[status(thm)],[202,209]) ).
thf(265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ( C
!= ( sdtmndt0 @ A @ B ) )
| ~ ( aElementOf0 @ D @ C )
| ( aElement0 @ D ) ),
inference(cnf,[status(esa)],[263]) ).
thf(277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElementOf0 @ D @ C )
| ( aElement0 @ D ) ),
inference(lifteq,[status(thm)],[265]) ).
thf(278,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElementOf0 @ C @ ( sdtmndt0 @ A @ B ) )
| ( aElement0 @ C ) ),
inference(simp,[status(thm)],[277]) ).
thf(31628,plain,
( ( ( slbdtrb0 @ xk )
!= xO )
| ( ( isFinite0 @ ( slbdtrb0 @ xk ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,19878]) ).
thf(31755,plain,
( ( ( slbdtrb0 @ xk )
!= xO )
| ( ( slbdtrb0 @ xk )
!= slcrc0 ) ),
inference(simp,[status(thm)],[31628]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElementOf0 @ B @ szNzAzT0 )
| ~ ( isFinite0 @ A )
| ~ ( sdtlseqdt0 @ B @ ( sbrdtbr0 @ A ) )
| ( aSubsetOf0 @ ( sk5 @ B @ A ) @ A ) ),
inference(cnf,[status(esa)],[221]) ).
thf(20717,plain,
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) ) )
!= ( isCountable0 @ xT ) ),
inference(paramod_ordered,[status(thm)],[20059,4360]) ).
thf(20770,plain,
( ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) )
!= xT ),
inference(simp,[status(thm)],[20717]) ).
thf(1661,plain,
! [A: $i] :
( ( aSubsetOf0 @ A @ A )
| ( ( aSet0 @ slcrc0 )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[372,135]) ).
thf(1662,plain,
aSubsetOf0 @ slcrc0 @ slcrc0,
inference(pattern_uni,[status(thm)],[1661:[bind(A,$thf( slcrc0 ))]]) ).
thf(24497,plain,
( ( xO != szNzAzT0 )
| ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
| ( ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
!= ( isCountable0 @ xO ) ) ),
inference(paramod_ordered,[status(thm)],[198,8213]) ).
thf(24553,plain,
( ( xO != szNzAzT0 )
| ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
| ( ( slbdtrb0 @ sk1 )
!= xO ) ),
inference(simp,[status(thm)],[24497]) ).
thf(5,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).
thf(111,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aSet0 @ B )
| ~ ( isFinite0 @ B )
| ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[111]) ).
thf(85,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ szNzAzT0 )
& ( isCountable0 @ B ) )
=> ! [C: $i] :
( ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= ( slbdtsldtrb0 @ B @ A ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) @ xT ) )
=> ( ( iLess0 @ A @ xK )
=> ? [D: $i] :
( ( aElementOf0 @ D @ xT )
& ? [E: $i] :
( ( aSubsetOf0 @ E @ B )
& ( isCountable0 @ E )
& ! [F: $i] :
( ( aElementOf0 @ F @ ( slbdtsldtrb0 @ E @ A ) )
=> ( ( sdtlpdtrp0 @ C @ F )
= D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3398) ).
thf(553,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ szNzAzT0 )
& ( isCountable0 @ B ) )
=> ! [C: $i] :
( ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= ( slbdtsldtrb0 @ B @ A ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) @ xT ) )
=> ( ( iLess0 @ A @ xK )
=> ? [D: $i] :
( ( aElementOf0 @ D @ xT )
& ? [E: $i] :
( ( aSubsetOf0 @ E @ B )
& ( isCountable0 @ E )
& ! [F: $i] :
( ( aElementOf0 @ F @ ( slbdtsldtrb0 @ E @ A ) )
=> ( ( sdtlpdtrp0 @ C @ F )
= D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(22952,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[1560,226]) ).
thf(22953,plain,
sdtlseqdt0 @ ( sk31 @ xK ) @ ( sk31 @ xK ),
inference(pattern_uni,[status(thm)],[22952:[bind(A,$thf( sk31 @ xK ))]]) ).
thf(78,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessSucc) ).
thf(487,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ! [C: $i] :
( ( C
= ( slbdtsldtrb0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aSubsetOf0 @ D @ A )
& ( ( sbrdtbr0 @ D )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
thf(458,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ! [C: $i] :
( ( ( C
= ( slbdtsldtrb0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aSubsetOf0 @ D @ A )
& ( ( sbrdtbr0 @ D )
= B ) ) )
& ( ( ( aSubsetOf0 @ D @ A )
& ( ( sbrdtbr0 @ D )
= B ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aSubsetOf0 @ D @ A )
& ( ( sbrdtbr0 @ D )
= B ) ) )
& ( ( ( aSubsetOf0 @ D @ A )
& ( ( sbrdtbr0 @ D )
= B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( slbdtsldtrb0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(818,plain,
( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
| ( ( szDzozmdt0 @ xc )
!= ( szDzozmdt0 @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[209,117]) ).
thf(823,plain,
( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
| ( xc != xd ) ),
inference(simp,[status(thm)],[818]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ( sk2 @ A @ B )
| ( aElementOf0 @ ( sk4 @ B @ A ) @ szNzAzT0 )
| ( B
= ( slbdtrb0 @ A ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( B
= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ( sk2 @ A @ B )
| ( aElementOf0 @ ( sk4 @ B @ A ) @ szNzAzT0 ) ),
inference(lifteq,[status(thm)],[171]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( B
= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ( sk2 @ A @ B )
| ( aElementOf0 @ ( sk4 @ B @ A ) @ szNzAzT0 ) ),
inference(simp,[status(thm)],[193]) ).
thf(1726,plain,
( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xc )
!= ( szDzozmdt0 @ xe ) ) ),
inference(paramod_ordered,[status(thm)],[167,1668]) ).
thf(1748,plain,
( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
| ( xc != xe ) ),
inference(simp,[status(thm)],[1726]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ~ ( aElement0 @ ( sk9 @ C @ B @ A ) )
| ~ ( aElementOf0 @ ( sk9 @ C @ B @ A ) @ A )
| ( ( sk9 @ C @ B @ A )
= B )
| ~ ( sk8 @ A @ B @ C )
| ( C
= ( sdtmndt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[263]) ).
thf(281,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk9 @ C @ B @ A )
= B )
| ( C
= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ~ ( aElement0 @ ( sk9 @ C @ B @ A ) )
| ~ ( aElementOf0 @ ( sk9 @ C @ B @ A ) @ A )
| ~ ( sk8 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[266]) ).
thf(282,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk9 @ C @ B @ A )
= B )
| ( C
= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ~ ( aElement0 @ ( sk9 @ C @ B @ A ) )
| ~ ( aElementOf0 @ ( sk9 @ C @ B @ A ) @ A )
| ~ ( sk8 @ A @ B @ C ) ),
inference(simp,[status(thm)],[281]) ).
thf(4366,plain,
( ( isCountable0 @ xT )
!= ( isCountable0 @ xO ) ),
inference(paramod_ordered,[status(thm)],[198,4360]) ).
thf(4377,plain,
xT != xO,
inference(simp,[status(thm)],[4366]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B )
& ( aSet0 @ C ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ C ) )
=> ( aSubsetOf0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
thf(150,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B )
& ( aSet0 @ C ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ C ) )
=> ( aSubsetOf0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1728,plain,
( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xc )
!= ( szDzozmdt0 @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[209,1668]) ).
thf(1743,plain,
( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
| ( xc != xd ) ),
inference(simp,[status(thm)],[1728]) ).
thf(31844,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
| ( ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[31786,166]) ).
thf(31845,plain,
( ( sdtlpdtrp0 @ xe @ ( szmzizndt0 @ szNzAzT0 ) )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) ) ) ),
inference(pattern_uni,[status(thm)],[31844:[bind(A,$thf( szmzizndt0 @ szNzAzT0 ))]]) ).
thf(4324,plain,
( ~ ( isFinite0 @ xS )
| ( ( aSet0 @ ( szDzozmdt0 @ xc ) )
!= ( aSet0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[1251,4286]) ).
thf(4346,plain,
( ~ ( isFinite0 @ xS )
| ( ( szDzozmdt0 @ xc )
!= xS ) ),
inference(simp,[status(thm)],[4324]) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ( B
!= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ C @ szNzAzT0 )
| ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A )
| ( aElementOf0 @ C @ B ) ),
inference(cnf,[status(esa)],[169]) ).
thf(181,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ C @ szNzAzT0 )
| ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A )
| ( aElementOf0 @ C @ B ) ),
inference(lifteq,[status(thm)],[174]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ szNzAzT0 )
| ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A )
| ( aElementOf0 @ B @ ( slbdtrb0 @ A ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(20236,plain,
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ xK ) )
!= ( isCountable0 @ slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[20056,647]) ).
thf(20287,plain,
( ( sdtlpdtrp0 @ xN @ xK )
!= slcrc0 ),
inference(simp,[status(thm)],[20236]) ).
thf(19063,plain,
! [A: $i] :
( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
| ( ( aElementOf0 @ sk1 @ xO )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[101,217]) ).
thf(19197,plain,
! [A: $i] :
( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
| ( sk1 != A )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[19063]) ).
thf(19248,plain,
( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ sk1 ) @ szNzAzT0 )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[19197]) ).
thf(31464,plain,
( ( ( slbdtrb0 @ xk )
!= szNzAzT0 )
| ( ( isFinite0 @ ( slbdtrb0 @ xk ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,19875]) ).
thf(31595,plain,
( ( ( slbdtrb0 @ xk )
!= szNzAzT0 )
| ( ( slbdtrb0 @ xk )
!= slcrc0 ) ),
inference(simp,[status(thm)],[31464]) ).
thf(20819,plain,
( ( xO != szNzAzT0 )
| ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ sk1 ) )
!= ( isCountable0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[20194,647]) ).
thf(20883,plain,
( ( xO != szNzAzT0 )
| ( ( sdtlpdtrp0 @ xN @ sk1 )
!= slcrc0 ) ),
inference(simp,[status(thm)],[20819]) ).
thf(1589,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( ( aElementOf0 @ sk1 @ szNzAzT0 )
!= ( aElementOf0 @ xk @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[508,848]) ).
thf(1642,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( sk1 != xk )
| ( szNzAzT0 != szNzAzT0 ) ),
inference(simp,[status(thm)],[1589]) ).
thf(1658,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( sk1 != xk ) ),
inference(simp,[status(thm)],[1642]) ).
thf(23083,plain,
( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
| ( sdtlseqdt0 @ sz00 @ xk )
| ( xk != xk ) ),
inference(paramod_ordered,[status(thm)],[873,22970]) ).
thf(23084,plain,
( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
| ( sdtlseqdt0 @ sz00 @ xk ) ),
inference(pattern_uni,[status(thm)],[23083:[]]) ).
thf(34100,plain,
! [A: $i] :
( ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31912,131]) ).
thf(34101,plain,
aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ) ),
inference(pattern_uni,[status(thm)],[34100:[bind(A,$thf( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ))]]) ).
thf(19680,plain,
( ~ ( isFinite0 @ ( slbdtrb0 @ xK ) )
| ( ( isCountable0 @ ( slbdtrb0 @ xK ) )
!= ( isCountable0 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[362,7840]) ).
thf(19738,plain,
( ~ ( isFinite0 @ ( slbdtrb0 @ xK ) )
| ( ( slbdtrb0 @ xK )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[19680]) ).
thf(31254,plain,
( ( ( slbdtrb0 @ xK )
!= szNzAzT0 )
| ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,19738]) ).
thf(31269,plain,
( ( ( slbdtrb0 @ xK )
!= szNzAzT0 )
| ( ( slbdtrb0 @ xK )
!= xT ) ),
inference(simp,[status(thm)],[31254]) ).
thf(64,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegFin) ).
thf(386,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(28872,plain,
( ( ( slbdtrb0 @ xK )
!= xS )
| ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,19731]) ).
thf(28978,plain,
( ( ( slbdtrb0 @ xK )
!= xS )
| ( ( slbdtrb0 @ xK )
!= slcrc0 ) ),
inference(simp,[status(thm)],[28872]) ).
thf(53,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElement0 @ ( sdtlpdtrp0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgElm) ).
thf(314,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElement0 @ ( sdtlpdtrp0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ! [C: $i] :
( ( ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ A @ B ) )
& ( isFinite0 @ C ) )
=> ? [D: $i] :
( ( aSubsetOf0 @ D @ A )
& ( isFinite0 @ D )
& ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelExtra) ).
thf(595,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ! [C: $i] :
( ( ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ A @ B ) )
& ( isFinite0 @ C ) )
=> ? [D: $i] :
( ( aSubsetOf0 @ D @ A )
& ( isFinite0 @ D )
& ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(608,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
!= sk1 )
| ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( aElementOf0 @ sk1 @ xO )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[101,102]) ).
thf(610,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
!= sk1 )
| ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( sk1 != A )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[608]) ).
thf(612,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ~ ( aElementOf0 @ sk1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[610]) ).
thf(24,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isCountable0 @ A )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCntRel) ).
thf(154,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(12856,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( ( szDzozmdt0 @ xC )
!= ( szDzozmdt0 @ xc ) ) ),
inference(paramod_ordered,[status(thm)],[454,7368]) ).
thf(12868,plain,
( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
| ( xC != xc ) ),
inference(simp,[status(thm)],[12856]) ).
thf(1725,plain,
( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
| ( ( szDzozmdt0 @ xN )
!= ( szDzozmdt0 @ xc ) ) ),
inference(paramod_ordered,[status(thm)],[593,1668]) ).
thf(1749,plain,
( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
| ( xN != xc ) ),
inference(simp,[status(thm)],[1725]) ).
thf(7783,plain,
! [A: $i] :
( ( ( sk31 @ xK )
= sz00 )
| ( aSet0 @ ( slbdtrb0 @ A ) )
| ( ( aElementOf0 @ ( sk31 @ ( sk31 @ xK ) ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[1571,186]) ).
thf(7784,plain,
( ( ( sk31 @ xK )
= sz00 )
| ( aSet0 @ ( slbdtrb0 @ ( sk31 @ ( sk31 @ xK ) ) ) ) ),
inference(pattern_uni,[status(thm)],[7783:[bind(A,$thf( sk31 @ ( sk31 @ xK ) ))]]) ).
thf(90,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ! [B: $i] :
( ( ( aElementOf0 @ B @ szNzAzT0 )
& ( B != sz00 ) )
=> ( isCountable0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelCSet) ).
thf(571,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ! [B: $i] :
( ( ( aElementOf0 @ B @ szNzAzT0 )
& ( B != sz00 ) )
=> ( isCountable0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(39762,plain,
! [A: $i] :
( ( aElementOf0 @ ( sk7 @ A ) @ xT )
| ( ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[31786,259]) ).
thf(39763,plain,
aElementOf0 @ ( sk7 @ ( szmzizndt0 @ szNzAzT0 ) ) @ xT,
inference(pattern_uni,[status(thm)],[39762:[bind(A,$thf( szmzizndt0 @ szNzAzT0 ))]]) ).
thf(7843,plain,
! [A: $i] :
( ( aSubsetOf0 @ A @ A )
| ( ( aSet0 @ ( slbdtrb0 @ xK ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7770,135]) ).
thf(7844,plain,
aSubsetOf0 @ ( slbdtrb0 @ xK ) @ ( slbdtrb0 @ xK ),
inference(pattern_uni,[status(thm)],[7843:[bind(A,$thf( slbdtrb0 @ xK ))]]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIHSort) ).
thf(203,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(92,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ~ ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( ( slbdtsldtrb0 @ A @ B )
!= slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelNSet) ).
thf(581,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ~ ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( ( slbdtsldtrb0 @ A @ B )
!= slcrc0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1593,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( ( aElementOf0 @ sk1 @ szNzAzT0 )
!= ( aElementOf0 @ xK @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[325,848]) ).
thf(1636,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( sk1 != xK )
| ( szNzAzT0 != szNzAzT0 ) ),
inference(simp,[status(thm)],[1593]) ).
thf(1654,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( sk1 != xK ) ),
inference(simp,[status(thm)],[1636]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isFinite0 @ A )
| ~ ( aSubsetOf0 @ B @ A )
| ( isFinite0 @ B ) ),
inference(cnf,[status(esa)],[103]) ).
thf(31870,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[31786,226]) ).
thf(31871,plain,
sdtlseqdt0 @ ( szmzizndt0 @ szNzAzT0 ) @ ( szmzizndt0 @ szNzAzT0 ),
inference(pattern_uni,[status(thm)],[31870:[bind(A,$thf( szmzizndt0 @ szNzAzT0 ))]]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aSet0 @ B )
| ( aElementOf0 @ A @ B )
| ( ( sdtmndt0 @ ( sdtpldt0 @ B @ A ) @ A )
= B ) ),
inference(cnf,[status(esa)],[229]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( ( sdtmndt0 @ ( sdtpldt0 @ B @ A ) @ A )
= B )
| ~ ( aElement0 @ A )
| ~ ( aSet0 @ B )
| ( aElementOf0 @ A @ B ) ),
inference(lifteq,[status(thm)],[230]) ).
thf(4729,plain,
! [A: $i] :
( ( ( sdtlpdtrp0 @ xe @ A )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
| ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[1560,166]) ).
thf(4730,plain,
( ( sdtlpdtrp0 @ xe @ ( sk31 @ xK ) )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) ) ) ),
inference(pattern_uni,[status(thm)],[4729:[bind(A,$thf( sk31 @ xK ))]]) ).
thf(34320,plain,
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) ) )
!= ( isCountable0 @ slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[31897,647]) ).
thf(34392,plain,
( ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) )
!= slcrc0 ),
inference(simp,[status(thm)],[34320]) ).
thf(32166,plain,
! [A: $i] :
( ( xO != szNzAzT0 )
| ( sdtlseqdt0 @ A @ A )
| ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[32083,226]) ).
thf(32236,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( xO != szNzAzT0 )
| ( ( szmzizndt0 @ xO )
!= A )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[32166]) ).
thf(32296,plain,
( ( sdtlseqdt0 @ ( szmzizndt0 @ xO ) @ ( szmzizndt0 @ xO ) )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[32236]) ).
thf(13216,plain,
( ( xC != xc )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,12868]) ).
thf(13224,plain,
( ( xC != xc )
| ( ( szDzozmdt0 @ xc )
!= xT ) ),
inference(simp,[status(thm)],[13216]) ).
thf(42469,plain,
( ( xk != sz00 )
| ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
!= ( isCountable0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[456,42399]) ).
thf(42551,plain,
( ( xk != sz00 )
| ( ( slbdtrb0 @ xk )
!= xS ) ),
inference(simp,[status(thm)],[42469]) ).
thf(1741,plain,
( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
| ( ( szDzozmdt0 @ xC )
!= ( szDzozmdt0 @ xc ) ) ),
inference(paramod_ordered,[status(thm)],[454,1668]) ).
thf(1745,plain,
( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
| ( xC != xc ) ),
inference(simp,[status(thm)],[1741]) ).
thf(31789,plain,
! [A: $i] :
( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
| ( ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[31786,217]) ).
thf(31790,plain,
aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) ) @ szNzAzT0,
inference(pattern_uni,[status(thm)],[31789:[bind(A,$thf( szmzizndt0 @ szNzAzT0 ))]]) ).
thf(7911,plain,
! [A: $i] :
( ( ( sbrdtbr0 @ A )
!= sz00 )
| ( A = slcrc0 )
| ( ( aSet0 @ ( slbdtrb0 @ xk ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7779,108]) ).
thf(7912,plain,
( ( ( sbrdtbr0 @ ( slbdtrb0 @ xk ) )
!= sz00 )
| ( ( slbdtrb0 @ xk )
= slcrc0 ) ),
inference(pattern_uni,[status(thm)],[7911:[bind(A,$thf( slbdtrb0 @ xk ))]]) ).
thf(7,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(114,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19076,plain,
! [A: $i] :
( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
| ( ( aElementOf0 @ xK @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[325,217]) ).
thf(19077,plain,
aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ xK ) @ szNzAzT0,
inference(pattern_uni,[status(thm)],[19076:[bind(A,$thf( xK ))]]) ).
thf(34344,plain,
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) ) )
!= ( isCountable0 @ xT ) ),
inference(paramod_ordered,[status(thm)],[31897,4360]) ).
thf(34402,plain,
( ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) )
!= xT ),
inference(simp,[status(thm)],[34344]) ).
thf(8252,plain,
! [A: $i] :
( ( xO != szNzAzT0 )
| ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ ( slbdtrb0 @ sk1 ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7814,131]) ).
thf(8253,plain,
( ( xO != szNzAzT0 )
| ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8252:[bind(A,$thf( slbdtrb0 @ sk1 ))]]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
<=> ( aSubsetOf0 @ ( slbdtrb0 @ A ) @ ( slbdtrb0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegLess) ).
thf(510,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
=> ( aSubsetOf0 @ ( slbdtrb0 @ A ) @ ( slbdtrb0 @ B ) ) )
& ( ( aSubsetOf0 @ ( slbdtrb0 @ A ) @ ( slbdtrb0 @ B ) )
=> ( sdtlseqdt0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(39617,plain,
! [A: $i] :
( ( xO != szNzAzT0 )
| ( aElementOf0 @ ( sk7 @ A ) @ xT )
| ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[32083,259]) ).
thf(39799,plain,
! [A: $i] :
( ( aElementOf0 @ ( sk7 @ A ) @ xT )
| ( xO != szNzAzT0 )
| ( ( szmzizndt0 @ xO )
!= A )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[39617]) ).
thf(39874,plain,
( ( aElementOf0 @ ( sk7 @ ( szmzizndt0 @ xO ) ) @ xT )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[39799]) ).
thf(207,plain,
aFunction0 @ xd,
inference(cnf,[status(esa)],[204]) ).
thf(20342,plain,
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ xk ) )
!= ( isCountable0 @ slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[20084,647]) ).
thf(20393,plain,
( ( sdtlpdtrp0 @ xN @ xk )
!= slcrc0 ),
inference(simp,[status(thm)],[20342]) ).
thf(676,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO )
| ( ( aElementOf0 @ sk1 @ szNzAzT0 )
!= ( aElementOf0 @ sz00 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[240,613]) ).
thf(681,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO )
| ( sk1 != sz00 )
| ( szNzAzT0 != szNzAzT0 ) ),
inference(simp,[status(thm)],[676]) ).
thf(684,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO )
| ( sk1 != sz00 ) ),
inference(simp,[status(thm)],[681]) ).
thf(273,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( sk8 @ A @ B @ C )
| ( aElement0 @ ( sk10 @ C @ B @ A ) )
| ( C
= ( sdtmndt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[263]) ).
thf(289,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( sk8 @ A @ B @ C )
| ( aElement0 @ ( sk10 @ C @ B @ A ) ) ),
inference(lifteq,[status(thm)],[273]) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aSet0 @ C )
| ( sk8 @ A @ B @ C )
| ( aElement0 @ ( sk10 @ C @ B @ A ) ) ),
inference(simp,[status(thm)],[289]) ).
thf(63,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
thf(378,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ A )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) ) )
& ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) )
=> ( aSubsetOf0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(214,plain,
! [A: $i] :
( ~ ( aFunction0 @ A )
| ~ ( isCountable0 @ ( szDzozmdt0 @ A ) )
| ~ ( isFinite0 @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) )
| ( isCountable0 @ ( sdtlbdtrb0 @ A @ ( szDzizrdt0 @ A ) ) ) ),
inference(cnf,[status(esa)],[213]) ).
thf(23075,plain,
( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
| ( sdtlseqdt0 @ sz00 @ xk )
| ( xk != xk ) ),
inference(paramod_ordered,[status(thm)],[7766,22970]) ).
thf(23076,plain,
( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
| ( sdtlseqdt0 @ sz00 @ xk ) ),
inference(pattern_uni,[status(thm)],[23075:[]]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aSet0 @ B )
| ~ ( aSet0 @ C )
| ~ ( aSubsetOf0 @ A @ B )
| ~ ( aSubsetOf0 @ B @ C )
| ( aSubsetOf0 @ A @ C ) ),
inference(cnf,[status(esa)],[150]) ).
thf(9287,plain,
( ( aSubsetOf0 @ ( slbdtrb0 @ xk ) @ slcrc0 )
| ( ( slbdtrb0 @ xk )
!= ( slbdtrb0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[137,7914]) ).
thf(9346,plain,
( ( aSubsetOf0 @ ( slbdtrb0 @ xk ) @ slcrc0 )
| ( xk != sz00 ) ),
inference(simp,[status(thm)],[9287]) ).
thf(71,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( isCountable0 @ B ) )
=> ( ! [C: $i,D: $i] :
( ( ( aElementOf0 @ C @ ( szDzozmdt0 @ A ) )
& ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( C != D ) )
=> ( ( sdtlpdtrp0 @ A @ C )
!= ( sdtlpdtrp0 @ A @ D ) ) )
=> ( isCountable0 @ ( sdtlcdtrc0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgCount) ).
thf(432,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( isCountable0 @ B ) )
=> ( ! [C: $i,D: $i] :
( ( ( aElementOf0 @ C @ ( szDzozmdt0 @ A ) )
& ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( C != D ) )
=> ( ( sdtlpdtrp0 @ A @ C )
!= ( sdtlpdtrp0 @ A @ D ) ) )
=> ( isCountable0 @ ( sdtlcdtrc0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ( aElementOf0 @ ( sk3 @ B @ A ) @ B )
| ~ ( sk2 @ A @ B )
| ( B
= ( slbdtrb0 @ A ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( B
= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ( aElementOf0 @ ( sk3 @ B @ A ) @ B )
| ~ ( sk2 @ A @ B ) ),
inference(lifteq,[status(thm)],[177]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( B
= ( slbdtrb0 @ A ) )
| ~ ( aElementOf0 @ A @ szNzAzT0 )
| ~ ( aSet0 @ B )
| ( aElementOf0 @ ( sk3 @ B @ A ) @ B )
| ~ ( sk2 @ A @ B ) ),
inference(simp,[status(thm)],[189]) ).
thf(13176,plain,
( ( xC != xc )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,12868]) ).
thf(13225,plain,
( ( xC != xc )
| ( ( szDzozmdt0 @ xc )
!= slcrc0 ) ),
inference(simp,[status(thm)],[13176]) ).
thf(59349,plain,
( ( xO != szNzAzT0 )
| ( sk1 != sz00 )
| ( ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
!= ( isCountable0 @ xO ) ) ),
inference(paramod_ordered,[status(thm)],[198,59208]) ).
thf(59420,plain,
( ( xO != szNzAzT0 )
| ( sk1 != sz00 )
| ( ( slbdtrb0 @ sk1 )
!= xO ) ),
inference(simp,[status(thm)],[59349]) ).
thf(98,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNoScLessZr) ).
thf(603,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(87,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( aSubsetOf0 @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) @ xT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4182) ).
thf(564,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( aSubsetOf0 @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) @ xT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(301,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
| ( C
!= ( sdtexdt0 @ A @ B ) )
| ( aFunction0 @ C ) ),
inference(cnf,[status(esa)],[298]) ).
thf(304,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( sdtexdt0 @ A @ B ) )
| ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
| ( aFunction0 @ C ) ),
inference(lifteq,[status(thm)],[301]) ).
thf(305,plain,
! [B: $i,A: $i] :
( ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
| ( aFunction0 @ ( sdtexdt0 @ A @ B ) ) ),
inference(simp,[status(thm)],[304]) ).
thf(58,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ? [B: $i] :
( ( aElementOf0 @ B @ xT )
& ? [C: $i] :
( ( aSubsetOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ C )
& ! [D: $i] :
( ( ( aSet0 @ D )
& ( aElementOf0 @ D @ ( slbdtsldtrb0 @ C @ xk ) ) )
=> ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ D )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4411) ).
thf(326,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ? [B: $i] :
( ( aElementOf0 @ B @ xT )
& ? [C: $i] :
( ( aSubsetOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ C )
& ! [D: $i] :
( ( ( aSet0 @ D )
& ( aElementOf0 @ D @ ( slbdtsldtrb0 @ C @ xk ) ) )
=> ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ D )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1362,plain,
! [A: $i] :
( ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ ( szDzozmdt0 @ xc ) )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1251,131]) ).
thf(1363,plain,
aElement0 @ ( sbrdtbr0 @ ( szDzozmdt0 @ xc ) ),
inference(pattern_uni,[status(thm)],[1362:[bind(A,$thf( szDzozmdt0 @ xc ))]]) ).
thf(4326,plain,
( ~ ( isFinite0 @ xS )
| ( ( aSet0 @ xS )
!= ( aSet0 @ xO ) ) ),
inference(paramod_ordered,[status(thm)],[199,4286]) ).
thf(4350,plain,
( ~ ( isFinite0 @ xS )
| ( xS != xO ) ),
inference(simp,[status(thm)],[4326]) ).
thf(31742,plain,
( ( ( slbdtrb0 @ xk )
!= xO )
| ( ( isFinite0 @ ( slbdtrb0 @ xk ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,19878]) ).
thf(31757,plain,
( ( ( slbdtrb0 @ xk )
!= xO )
| ( ( slbdtrb0 @ xk )
!= xT ) ),
inference(simp,[status(thm)],[31742]) ).
thf(34837,plain,
( ( xN != xe )
| ( aElementOf0 @ xS @ xS )
| ( ( szmzizndt0 @ xS )
!= ( szmzizndt0 @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[5164,34726]) ).
thf(34838,plain,
( ( xN != xe )
| ( aElementOf0 @ xS @ xS ) ),
inference(pattern_uni,[status(thm)],[34837:[]]) ).
thf(39615,plain,
! [A: $i] :
( ( xk = sz00 )
| ( aElementOf0 @ ( sk7 @ A ) @ xT )
| ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[873,259]) ).
thf(39616,plain,
( ( xk = sz00 )
| ( aElementOf0 @ ( sk7 @ ( sk31 @ xk ) ) @ xT ) ),
inference(pattern_uni,[status(thm)],[39615:[bind(A,$thf( sk31 @ xk ))]]) ).
thf(1729,plain,
( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
| ( ( szDzozmdt0 @ xc )
!= ( szDzozmdt0 @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[209,1668]) ).
thf(1742,plain,
( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
| ( xc != xd ) ),
inference(simp,[status(thm)],[1729]) ).
thf(274,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ( C
!= ( sdtmndt0 @ A @ B ) )
| ( aSet0 @ C ) ),
inference(cnf,[status(esa)],[263]) ).
thf(293,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( sdtmndt0 @ A @ B ) )
| ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ( aSet0 @ C ) ),
inference(lifteq,[status(thm)],[274]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( aElement0 @ B )
| ( aSet0 @ ( sdtmndt0 @ A @ B ) ) ),
inference(simp,[status(thm)],[293]) ).
thf(1606,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( ( aElementOf0 @ sk1 @ szNzAzT0 )
!= ( aElementOf0 @ sz00 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[240,848]) ).
thf(1639,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( sk1 != sz00 )
| ( szNzAzT0 != szNzAzT0 ) ),
inference(simp,[status(thm)],[1606]) ).
thf(1657,plain,
( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
| ( aElementOf0 @ sz00 @ xO )
| ( sk1 != sz00 ) ),
inference(simp,[status(thm)],[1639]) ).
thf(5092,plain,
( ( ( szmzizndt0 @ xS )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= szNzAzT0 ) ),
inference(rewrite,[status(thm)],[689,5090]) ).
thf(733,plain,
( ( ( sdtlpdtrp0 @ xe @ xK )
!= sk1 )
| ( ( aElementOf0 @ xK @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
!= ( aElementOf0 @ xK @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[325,695]) ).
thf(737,plain,
( ( ( sdtlpdtrp0 @ xe @ xK )
!= sk1 )
| ( xK != xK )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[733]) ).
thf(740,plain,
( ( ( sdtlpdtrp0 @ xe @ xK )
!= sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[737]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtlbdtrb0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPtt) ).
thf(332,plain,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtlbdtrb0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) ) )
& ( ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) ) )
& ( ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtlbdtrb0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(816,plain,
( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
| ( ( szDzozmdt0 @ xC )
!= ( szDzozmdt0 @ xc ) ) ),
inference(paramod_ordered,[status(thm)],[454,117]) ).
thf(822,plain,
( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
| ( xC != xc ) ),
inference(simp,[status(thm)],[816]) ).
thf(3885,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ sz00 )
= xK )
| ( A = sz00 )
| ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
| ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[3358,517]) ).
thf(3886,plain,
( ( ( szszuzczcdt0 @ sz00 )
= xK )
| ( ( sk31 @ xk )
= sz00 )
| ( aElementOf0 @ ( sk31 @ ( sk31 @ xk ) ) @ szNzAzT0 ) ),
inference(pattern_uni,[status(thm)],[3885:[bind(A,$thf( sk31 @ xk ))]]) ).
thf(73,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(442,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(622,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ( xO != szNzAzT0 )
| ( ( aElementOf0 @ sk1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
!= ( aElementOf0 @ sk1 @ xO ) ) ),
inference(paramod_ordered,[status(thm)],[101,612]) ).
thf(623,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ( xO != szNzAzT0 )
| ( sk1 != sk1 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO ) ),
inference(simp,[status(thm)],[622]) ).
thf(624,plain,
( ( ( sdtlpdtrp0 @ xe @ sk1 )
!= sk1 )
| ( xO != szNzAzT0 )
| ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
!= xO ) ),
inference(simp,[status(thm)],[623]) ).
thf(9570,plain,
( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
| ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ sz00 ) ) )
| ( xk != xk ) ),
inference(paramod_ordered,[status(thm)],[7766,7943]) ).
thf(9571,plain,
( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
| ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[9570:[]]) ).
thf(22079,plain,
( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
| ( aElement0 @ ( sbrdtbr0 @ slcrc0 ) ) ),
inference(rewrite,[status(thm)],[9571,137]) ).
thf(24496,plain,
( ( xO != szNzAzT0 )
| ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
| ( ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
!= ( isCountable0 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[362,8213]) ).
thf(24559,plain,
( ( xO != szNzAzT0 )
| ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
| ( ( slbdtrb0 @ sk1 )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[24496]) ).
thf(28966,plain,
( ( ( slbdtrb0 @ xK )
!= xS )
| ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
!= ( isFinite0 @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[146,19731]) ).
thf(28982,plain,
( ( ( slbdtrb0 @ xK )
!= xS )
| ( ( slbdtrb0 @ xK )
!= xT ) ),
inference(simp,[status(thm)],[28966]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( aSubsetOf0 @ B @ szNzAzT0 )
& ( A != slcrc0 )
& ( B != slcrc0 ) )
=> ( ( ( aElementOf0 @ ( szmzizndt0 @ A ) @ B )
& ( aElementOf0 @ ( szmzizndt0 @ B ) @ A ) )
=> ( ( szmzizndt0 @ A )
= ( szmzizndt0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMinMin) ).
thf(322,plain,
! [A: $i,B: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( aSubsetOf0 @ B @ szNzAzT0 )
& ( A != slcrc0 )
& ( B != slcrc0 ) )
=> ( ( ( aElementOf0 @ ( szmzizndt0 @ A ) @ B )
& ( aElementOf0 @ ( szmzizndt0 @ B ) @ A ) )
=> ( ( szmzizndt0 @ A )
= ( szmzizndt0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1366,plain,
! [A: $i] :
( ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ xO )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[199,131]) ).
thf(1367,plain,
aElement0 @ ( sbrdtbr0 @ xO ),
inference(pattern_uni,[status(thm)],[1366:[bind(A,$thf( xO ))]]) ).
thf(215,plain,
! [A: $i] :
( ~ ( aFunction0 @ A )
| ~ ( isCountable0 @ ( szDzozmdt0 @ A ) )
| ~ ( isFinite0 @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) )
| ( aElement0 @ ( szDzizrdt0 @ A ) ) ),
inference(cnf,[status(esa)],[213]) ).
thf(22949,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aElementOf0 @ xK @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[325,226]) ).
thf(22950,plain,
sdtlseqdt0 @ xK @ xK,
inference(pattern_uni,[status(thm)],[22949:[bind(A,$thf( xK ))]]) ).
thf(22980,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aElementOf0 @ sz00 @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[240,226]) ).
thf(22981,plain,
sdtlseqdt0 @ sz00 @ sz00,
inference(pattern_uni,[status(thm)],[22980:[bind(A,$thf( sz00 ))]]) ).
thf(13056,plain,
( ( xN != xc )
| ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
!= ( isFinite0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[115,12865]) ).
thf(13107,plain,
( ( xN != xc )
| ( ( szDzozmdt0 @ xc )
!= slcrc0 ) ),
inference(simp,[status(thm)],[13056]) ).
thf(20361,plain,
( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ xk ) )
!= ( isCountable0 @ xT ) ),
inference(paramod_ordered,[status(thm)],[20084,4360]) ).
thf(20404,plain,
( ( sdtlpdtrp0 @ xN @ xk )
!= xT ),
inference(simp,[status(thm)],[20361]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ( A = slcrc0 )
| ~ ( aElementOf0 @ B @ A )
| ~ ( sdtlseqdt0 @ B @ ( sk6 @ B @ A ) )
| ( B
= ( szmzizndt0 @ A ) ) ),
inference(cnf,[status(esa)],[242]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( A = slcrc0 )
| ( B
= ( szmzizndt0 @ A ) )
| ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ A )
| ~ ( sdtlseqdt0 @ B @ ( sk6 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[246]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( A = slcrc0 )
| ( B
= ( szmzizndt0 @ A ) )
| ~ ( aSubsetOf0 @ A @ szNzAzT0 )
| ~ ( aElementOf0 @ B @ A )
| ~ ( sdtlseqdt0 @ B @ ( sk6 @ B @ A ) ) ),
inference(simp,[status(thm)],[253]) ).
thf(303,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
| ~ ( aFunction0 @ C )
| ( ( szDzozmdt0 @ C )
!= B )
| ( aElementOf0 @ ( sk11 @ C @ B @ A ) @ B )
| ( C
= ( sdtexdt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[298]) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( ( szDzozmdt0 @ C )
!= B )
| ( C
= ( sdtexdt0 @ A @ B ) )
| ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
| ~ ( aFunction0 @ C )
| ( aElementOf0 @ ( sk11 @ C @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[303]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( ( sdtexdt0 @ A @ ( szDzozmdt0 @ B ) )
= B )
| ~ ( aFunction0 @ A )
| ~ ( aSubsetOf0 @ ( szDzozmdt0 @ B ) @ ( szDzozmdt0 @ A ) )
| ~ ( aFunction0 @ B )
| ( aElementOf0 @ ( sk11 @ B @ ( szDzozmdt0 @ B ) @ A ) @ ( szDzozmdt0 @ B ) ) ),
inference(simp,[status(thm)],[308]) ).
thf(20085,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ sz00 )
= xK )
| ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
| ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[3358,218]) ).
thf(20086,plain,
( ( ( szszuzczcdt0 @ sz00 )
= xK )
| ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xk ) ) ) ),
inference(pattern_uni,[status(thm)],[20085:[bind(A,$thf( sk31 @ xk ))]]) ).
thf(22941,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aElementOf0 @ sk1 @ xO )
!= ( aElementOf0 @ A @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[101,226]) ).
thf(23011,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( sk1 != A )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[22941]) ).
thf(23022,plain,
( ( sdtlseqdt0 @ sk1 @ sk1 )
| ( xO != szNzAzT0 ) ),
inference(simp,[status(thm)],[23011]) ).
thf(4871,plain,
( ( ( sdtlpdtrp0 @ xe @ xk )
= ( szmzizndt0 @ xS ) )
| ( ( sdtlpdtrp0 @ xN @ xk )
!= ( sdtlpdtrp0 @ xN @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[594,4711]) ).
thf(4928,plain,
( ( ( sdtlpdtrp0 @ xe @ xk )
= ( szmzizndt0 @ xS ) )
| ( xN != xN )
| ( xk != sz00 ) ),
inference(simp,[status(thm)],[4871]) ).
thf(4940,plain,
( ( ( sdtlpdtrp0 @ xe @ xk )
= ( szmzizndt0 @ xS ) )
| ( xk != sz00 ) ),
inference(simp,[status(thm)],[4928]) ).
thf(147484,plain,
$false,
inference(cvc4,[status(thm)],[20194,7766,101,34726,14220,1369,138,518,7990,29267,8030,34103,234,9573,115,20056,9351,69974,7368,120,7781,202,3382,4714,59412,4376,217,276,4711,873,3745,22970,32083,797,814,24560,35134,7873,12921,12865,1354,153,1746,34039,39684,68752,417,288,19069,1265,32270,257,320,8025,7914,184,372,587,20059,4349,24558,59208,196,157,38320,7945,18333,284,325,228,316,261,1379,39711,421,20772,152,12864,216,20890,7786,1664,38307,591,321,7376,121,574,19113,18786,821,602,147,280,221,29118,132,42399,660,116,428,32288,133,307,292,248,117,439,20084,39650,59415,12927,220,102,798,7814,201,13104,4557,7703,34898,4375,160,297,192,429,137,165,729,1560,19082,252,19886,456,19731,224,229,8255,566,197,20047,361,7842,3254,156,388,13163,593,141,188,1672,19879,1361,1182,3728,489,7365,69954,225,1659,4721,38100,42554,39632,23078,1744,212,706,42396,647,8219,12859,10834,654,1668,29114,457,129,503,13167,569,134,237,105,7770,508,20290,19878,12361,23086,5090,30911,311,1251,425,824,166,148,1747,161,444,7910,375,513,24557,3358,39888,180,296,149,7372,584,562,423,22945,286,20310,826,12862,204,259,313,144,50265,7875,4573,42546,236,32088,12867,19881,19875,19741,159,31590,113,219,736,31897,3710,509,1175,362,451,4374,208,1571,599,14223,103,594,213,848,240,18912,155,198,108,130,827,695,278,31755,223,135,241,167,455,19734,226,20770,1662,24553,162,374,255,112,553,22953,209,487,7773,123,458,823,194,145,1748,4360,282,4377,150,1743,31845,4346,199,182,20287,19248,31595,20883,127,1658,23084,34101,31269,4145,7779,613,386,1670,28978,314,595,612,69578,154,12868,1749,7374,7784,446,571,143,39763,7844,99,363,203,581,1654,218,104,31871,250,231,4730,34392,32296,517,319,13224,19738,42551,258,158,7840,186,1745,31790,781,7912,114,19077,34402,8253,235,510,39874,207,20393,684,290,119,5164,378,716,214,23076,31912,151,9346,432,146,31786,190,13225,59420,603,168,262,564,305,210,326,239,1363,4350,4286,506,31757,34838,7943,39616,19733,1742,294,136,1657,5092,740,332,8213,822,131,3886,200,691,442,607,624,22079,24559,28982,322,122,1367,215,22950,22981,364,4298,13107,111,20404,254,227,309,20086,23022,454,4940,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM600+1 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n003.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 20 06:27:39 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.41/1.03 % [INFO] Parsing done (159ms).
% 1.41/1.03 % [INFO] Running in sequential loop mode.
% 1.86/1.24 % [INFO] eprover registered as external prover.
% 1.86/1.24 % [INFO] cvc4 registered as external prover.
% 1.86/1.24 % [INFO] Scanning for conjecture ...
% 2.07/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.36 % [INFO] Found a conjecture (or negated_conjecture) and 96 axioms. Running axiom selection ...
% 2.53/1.42 % [INFO] Axiom selection finished. Selected 96 axioms (removed 0 axioms).
% 2.59/1.44 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.47 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.47 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.47 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.47 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.48 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.48 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.48 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.49 % [INFO] Problem is first-order (TPTP FOF).
% 2.59/1.50 % [INFO] Type checking passed.
% 2.59/1.50 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 90.58/36.86 % External prover 'cvc4' found a proof!
% 90.58/36.86 % [INFO] Killing All external provers ...
% 90.58/36.86 % Time passed: 36326ms (effective reasoning time: 35819ms)
% 90.58/36.86 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 90.58/36.86 % Axioms used in derivation (96): mDefSel, mFunSort, mZeroNum, mSubASymm, mCardEmpty, m__3533, mImgRng, mSuccLess, mCountNFin, mSegLess, m__4331, mCardSubEx, mDefEmp, m__3435, mFinSubSeg, m__4660, mIHSort, m__3965, mDefSImg, m__4758, mDiffCons, mSubRefl, mDefMin, mSubFSet, mEOfElem, m__3398, mDefDiff, mSelCSet, m__4182, m__3462, mSetSort, mCardS, mSegZero, mSuccEquSucc, m__4730, m__3821, mSelNSet, mDomSet, mSegSucc, mLessSucc, mIH, mFDiffSet, m__3754, mCDiffSet, mFinRel, mSegFin, mDefCons, mNoScLessZr, m__4854, mConsDiff, m__3520, mLessRefl, mLessRel, mDefSeg, mCardSub, mCountNFin_01, m__4891, mCardNum, m__3291, mImgElm, mDefPtt, mImgCount, mLessASymm, mDirichlet, mMinMin, m__4908, mSelFSet, mNatNSucc, mDefMax, m__3453, m__3671, mEmpFin, mLessTotal, mNATSet, mFConsSet, mElmSort, mCardDiff, mZeroLess, mPttSet, mSelSub, mDefSub, mLessTrans, mNatExtra, m__4411, mSuccNum, mSubTrans, m__4618, mCntRel, mSelExtra, m__3418, m__3623, m__4151, mCardCons, mDefRst, mCConsSet, mCardSeg
% 90.58/36.86 % No. of inferences in proof: 932
% 90.58/36.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 36326 ms resp. 35819 ms w/o parsing
% 91.04/37.00 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 91.04/37.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------